Range pattern definition of susceptibility of layout regions to fabrication issues

ABSTRACT

A memory is encoded with a data structure that represents a pattern having a range for one or more dimensions and/or positions of line segments therein. The data structure identifies two or more line segments that are located at a boundary of the pattern. The data structure also includes at least one set of values that identify a maximum limit and a minimum limit (i.e. the range) between which relative location and/or dimension of an additional line segment of the pattern in a portion of a layout of an integrated circuit (IC) chip, represents a defect in the IC chip when fabricated. In most embodiments, multiple ranges are specified in such a range defining pattern for example a width range is specified for the width of a trace of material in the layout and a spacing range is specified for the separation distance between two adjacent traces in the layout.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to and incorporates by reference herein inits entirety a commonly owned patent application entitled “IDENTIFYINGLAYOUT REGIONS SUSCEPTIBLE TO FABRICATION ISSUES BY USING RANGEPATTERNS” that is being concurrently filed herewith by SubarnarekhaSinha, Hailong Yao, and Charles C. Chiang.

BACKGROUND

1. Field of the Invention

The invention relates to design of layouts used in fabrication ofsemiconductor wafers. More specifically, the invention relates to amethod and an apparatus for representing several patterns, which aresimilar to one another and that may be improperly fabricated in anintegrated circuit (IC) chip, as a data structure (“range pattern”)containing a pattern having range(s) on dimension(s) of the pattern.

2. Related Art

In the manufacture of integrated circuit (IC) chips, minimum featuresizes have been shrinking according to Moore's law. Currently theminimum feature size is smaller than the wavelength of light used in theoptical imaging system. Accordingly it has become increasingly difficultto achieve reasonable fidelity (including resolution and depth of focus)between (a) a layout as designed in a computer and (b) shapes of circuitelements formed in a wafer after fabrication (which normally involves anumber of processes such as photolithography followed by Cu depositionand chemical mechanical polishing). A number of reticle enhancementtechnologies (RET) such as optical proximity correction (OPC), phaseshifting masks (PSM), and sub-resolution assist features (SRAF) areunable to overcome such fabrication issues. For example, even after alayout (FIG. 1A and FIG. 1D) is OPC corrected (FIG. 1B and 1E), theresulting shape in a fabricated wafer (FIG. 1C and 1F) may have one ormore defects (e.g. Wpinch falls below a minimum limit, and causes anopen circuit failure in the IC chip).

Current technology (prior to the invention described below) addressessuch fabrication issues by application of design rules that aretypically specified by a fabrication facility (“fab”). However, use ofsuch fab-specified design rules can result in over-specification of thedesign or an unnecessarily large number of defects from fabricationthereby reducing yield. The following two articles have attempted toquantify the amount of RET (e.g. in the form of OPC) that a routedlayout requires and modify the routing such that the burden of masksynthesis tools is reduced: [1] L-D. Huang, M. D. F. Wong: OpticalProximity Correction (OPC)-Friendly Maze Routing, DAC 2004; and [2] J.Mitra, P. Yu, D. Pan: RADAR: RET-aware detailed routing using fastlithography simulations, DAC 2005.

In such a framework, it is typical for regions of a layout that requirelarge amounts of RET to be tagged as hotspots. Since it is very timeconsuming to accurately estimate the amount of RET that a particularrouted layout needs without performing the actual operation on designs(performing RET takes about 20-30 hours of simulation time for a1-million gate design, when using a personal computer (PC) with acentral processing unit (CPU) operating at 1 GHz and equipped with 1 GBmemory), such methods typically use a simple aerial image simulator tofind geometric shapes in the layout that are expected to print badly.Consequently, these methods lack the ability to factor in RETinformation when identifying potential hotspots.

Inventors of the invention described below have realized that currentmethods overestimate the number of hotspots due to failure to use RETinformation as well as failure to use details of mask synthesis (whichmay not be available due to intellectual property (IP) issues from useof third party designs, e.g. if hard IP cores are present in an ICdesign). Hence, layout geometries that can be easily corrected in a RETstage and/or mask synthesis stage typically get tagged by currentmethods as hotspots to be corrected during the layout routing stage.Correcting all the tagged hotspots in the layout routing stage resultsin overly-conservative, less than optimal routing design.

SUMMARY

A computer, when appropriately programmed in accordance with theinvention, contains in its memory at least one data structure (alsocalled “range pattern”) representing an arrangement of line segmentsrelative to one another and a range for the position and/or dimension ofone or more line segments. For example, a width range and/or a lengthrange for a rectangle is a range on the corresponding dimension (widthand/or length) of a line segment whereas a spacing range is an exampleof a range on the position of one line segment relative to another linesegment. Specifically, in several embodiments of the invention, at leastone such data structure identifies at least two line segments that arelocated at two fixed boundaries of the range pattern and are orientedperpendicular to one another (e.g. left and bottom boundaries). Inaddition, the data structure includes at least one pair of values thatidentify a maximum limit and a minimum limit (i.e. a range). If anadditional line segment in the range pattern is positioned between theselimits (relative to one of the line segments in the range pattern) in aportion of a layout of an integrated circuit (IC) chip, then thatportion represents a region susceptible to fabrication issues in the ICchip. In most embodiments of the data structure, multiple ranges arespecified for corresponding multiple dimensions and/or multiple relativepositions of line segments in the range pattern, for example a widthrange is specified for the width of a trace in the range pattern and aspacing range is specified for a distance between two traces adjacent toone another in the range pattern.

Many embodiments of a method and apparatus in accordance with theinvention use a single range pattern of the type described above tocompactly represent numerous patterns in an IC layout that are similarto one another in many respects but differ from one another in theposition of a small number of line segments. Specifically, appropriateranges are selected for appropriate dimensions (either manually orautomatically), to define a single range pattern (or a handful of rangepatterns) to compactly represent said numerous patterns (withoutexplicitly describing each of the numerous patterns individually).Grouping of multiple patterns into a single range pattern eliminates theneed for memory otherwise required in the prior art to represent eachpattern individually.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrate a prior art layout after routing and afteroptical proximity correction (OPC) while FIG. 1C illustrates a structureresulting after fabrication.

FIGS. 1D, 1E and 1F illustrate the steps of FIGS. 1A-1C for anotherprior art layout.

FIGS. 2A-2C illustrate a “drill” range pattern that, in accordance withthe invention, has a width range (Wmin, Wmax) and a spacing S.

FIG. 2D illustrates, in a block diagram, a data structure 210 for arange pattern in a computer memory in accordance with the invention.

FIG. 2E illustrates the drill range pattern (shown in dotted lines) ofFIGS. 2A-2C with additional ranges.

FIGS. 2F and 2G illustrate two patterns covered by the drill rangepattern of FIG. 2E.

FIGS. 2H and 2J illustrate, in block diagrams, two embodiments of thedata structure of FIG. 2D.

FIG. 2I illustrates a “staircase” range pattern in accordance with theinvention that, in addition to width and spacing ranges, has a lengthrange (Lmin, Lmax) for a middle trace, as well as a constraint (<Omax)on overlap between ends of two traces between which the middle trace islocated.

FIG. 3A illustrates, in a flow chart, a process of creating a rangepattern in accordance with the invention.

FIG. 3B illustrates, in a flow chart, an alternative to the process inFIG. 3A, whereby a human who is experienced in IC fabrication, suppliesto a computer the data for creating a range pattern based on the human'sexperience.

FIG. 3C illustrates, in a flow chart, a method for performinglithography aware routing by using one or more range pattern(s), in someembodiments of the invention.

FIG. 4A illustrates a re-routed layout in a location that previously hada lithography hotspot in the form of a staircase pattern that matchedthe range pattern illustrated in FIG. 2I.

FIG. 4B illustrates traces that result from fabrication of the re-routedlayout of FIG. 4A.

FIG. 5A illustrates slicing of the staircase range pattern of FIG. 21.

FIGS. 5B illustrates a “door” range pattern, and FIGS. 5C-5F illustratefour sliced versions of the range pattern shown in FIG. 5B.

FIG. 5G illustrates, a sliced version of a “mountain” range pattern, inaccordance with the invention.

FIG. 5H illustrates, in a flow chart, matching a block of a layout to asliced version of a range pattern in accordance with the invention.

FIG. 5I illustrates the flow chart of FIG. 5H that is used in analternative embodiment also in accordance with the invention.

FIGS. 6A and 6F illustrate, in flow charts of some embodiments, twomethods of matching layout blocks to range patterns that are performedin a hierarchical manner, using a coarse grid and a fine gridrespectively.

FIGS. 6B and 6C illustrate digitization of a block of a layout by use ofa grid that is performed in many embodiments of the invention.

FIGS. 6D and 6E illustrate, in a graph, a window shifting strategy usedin some embodiments of the invention to ensure that consecutive windowsoverlap to avoid missing matches of range patterns to layout regions.

FIG. 6G illustrates, in a graph, worm-like movement of a layout block insome embodiments of the invention.

FIG. 7 illustrates slicing of a block of a layout in some embodiments ofthe invention.

FIG. 8A illustrates, in a flow chart, acts performed in accordance withthe invention, to slice a range pattern, followed by comparison of thepattern slices resulting therefrom, with a sliced version of the blockof the layout.

FIG. 8B illustrates, in a block diagram, a data structure for a slicedversion of a range pattern in a computer memory in accordance with theinvention.

FIGS. 8C and 8D illustrate matrices of adjacency data (“adjacencymatrix”) for horizontal and vertical edges respectively of a slicedversion of a range pattern generated from user-provided data which issupplied as input to the method of FIG. 9A

FIG. 8E illustrates one specific embodiment of the method in shown inFIG. 8A.

FIG. 9A illustrates, in a flow chart, a method of computing a range forthe distance between one or more pairs of line segments in a pattern, byuse of the Floyd Warshall algorithm.

FIGS. 9B and 9C illustrate adjacency matrices for horizontal andvertical edges that are output by the method of FIG. 9A based oncorresponding inputs shown in FIGS. 8C and 8D.

FIGS. 10A and 10B illustrate, in flow charts, methods for counting andenumerating the number of cutting slices of a range pattern.

FIG. 10C illustrates, in a flow chart, a method of computing ranges ofdimensions of slices in a sliced version of a range pattern.

FIG. 11A illustrates, in a flow chart, a method for matching a rangepattern to an IC layout.

FIGS. 11B and 11D illustrate, in flow charts, methods for matching asliced version of the range pattern to a block in a layout that aredigitized using a coarse grid and a fine grid respectively.

FIG. 11C illustrates, in program, two different block sizes that areused in the flowcharts of FIGS. 11B and 11D.

FIG. 12A illustrates, in a flow chart, a method for mapping a cuttingslice on to a grid of a specified size, in some embodiments of theinvention.

FIG. 12B illustrates, in a flow chart, a method of encoding a cuttingslice, in some embodiments of the invention.

FIG. 13A illustrates, in a flow chart, a method of matching a rangepattern to a layout, at the slice level, in some embodiments of theinvention.

FIGS. 13B and 13C illustrate, in flow charts, a method of comparing twoone dimensional strings, by applying the KMP string matching algorithmto encoded strings of slices of a layout and of a range pattern, in someembodiments of the invention.

FIG. 13D illustrates, in a flow chart, a method of verifing at the finelevel, a potential match of a range pattern to a block in the layoutthat has been identified by use of a coarse grid, in some embodiments ofthe invention.

FIG. 14A illustrates, in a block diagram, optional software that may beincluded in a computer that has been programmed with a range patternmatcher and hotspot display software in some embodiments of theinvention.

FIG. 14B illustrates, a simplified representation of an exemplarydigital ASIC design flow in accordance with the invention.

FIGS. 15A and 15B together illustrate a pattern format file that is usedin some embodiments of the invention, to specify a pattern in thecutting slice representation.

FIGS. 16-19 illustrate, in flow charts, acts performed by a single gridmethod in some embodiments of the invention

DETAILED DESCRIPTION

A computer, when appropriately programmed in accordance with theinvention, contains in memory at least one data structure to representnumerous patterns compactly. The data structure (called “range pattern”)typically identifies the relative location of pairs of line segments inthe patterns using a range, such as a width range for a rectangle in thepattern, as illustrated in FIG. 2A. In the example illustrated in FIG.2A, a range pattern 200 represents an arrangement of two traces orientedperpendicular to one another, in the form of an inverted letter “T” ofthe English Alphabet with the two traces separated from one another by aspacing distance S. The horizontal trace in this example is representedin range pattern 200 by a rectangle 201 of fixed dimensions. Thevertical trace in this example is represented by a rectangle 202 offixed length L but the width of rectangle 202 can be any value withinthe range (called “width range”) defined by two values, namely a minimumlimit Wmin and a maximum limit Wmax. For this reason, rectangle 202 canbe either one of two rectangles 202A and 202N in FIG. 2A that have therespective widths Wmin and Wmax, and hence range pattern 200 representsat least two patterns, namely a first pattern formed by rectangles 201and 202A and a second pattern formed by rectangles 201 and 202B.

In fact, as illustrated in FIG. 2B, the vertical rectangle 202 in thejust-described range pattern 200 represents a number of additionalrectangles 202I-202J whose width W is between Wmin and Wmax, whereinA≦I≦J≦N, N being the total number of rectangles represented in the rangepattern; note that N is theoretically infinite but in practice islimited by the smallest dimension obtainable from IC fabrication. Thissmallest dimension in turn depends on the size of the manufacturing gridof an integrated circuit's layout.

Note that although a single range has been described above in referenceto the range pattern illustrated in FIGS. 2A and 2B, most embodiments ofrange patterns have more than one range, for example as illustrated inFIG. 2C by width ranges on each of the rectangles in the range pattern.In this example shown in FIG. 2C, all dimensions are same as in FIGS. 2Aand 2B except that the width of the horizontal rectangle is now definedto have the same range as the vertical rectangle, i.e. between minimumlimit Wmin and maximum limit Wmax. Therefore, in a manner similar tocoverage of N vertical rectangles 202A-202N by the width range on thevertical rectangle, the newly defined width range on the horizontalrectangle now covers N horizontal rectangles 201A-201N. Hence, the rangepattern illustrated in FIG. 2C now covers all possible pairs ofhorizontal and vertical rectangles that have widths in the range Wminand Wmax, i.e. a total of N×N patterns.

The variability of width of both the horizontal rectangle and thevertical rectangle in the pattern 200 as illustrated in FIG. 2C iscaptured in some embodiments by use of a data structure 210 to accesscomputer memory illustrated in FIG. 2D that (a) identifies one or moreline segments that are located at one or more known locations within therange pattern in a store 214 and (b) identifies a range (of minimum andmaximum limits on the dimension or relative position) for an additionalline segment in the range pattern in another store 215. Note that therelative position of the additional line segment is with respect to oneof the line segments in the range pattern. Furthermore, dimensions ofthe range pattern other than width may also have ranges specifiedthereon, e.g. a spacing range is illustrated in FIG. 2E. Also, eachrange in a range pattern may be specified independent of another rangein the range pattern, e.g. as illustrated in FIG. 2E by one width rangebetween Wmin201 to Wmax201 for horizontal rectangle 201 and anotherwidth range between Wmin202 to Wmax202 for vertical rectangle 202. Insome other embodiments, ranges can be specified on the distance betweensets of line segments.

The just-described known location(s) can be based on any property thatis normally inherent in a pattern, such as a pattern's center or apattern's boundary depending on the embodiment. Also depending on theembodiment, the pattern (which is used to define the known location) canbe selected (based on respective ranges in the range pattern) to haveminimum dimensions or maximum dimensions or average dimensions (e.g. aminimum pattern as illustrated in FIG. 2F or a maximum pattern asillustrated in FIG. 2G, or an average pattern which is not shown). Theranges may be identified, relative to any known location(s) byidentifying one or more line segments of the range pattern, anddetermining how they vary relative to the known location(s).

As noted elsewhere, stores 214 and 215 are included in a memory of acomputer in accordance with the invention. Each of stores 214 and 215may contain several storage locations, depending on the embodiment. Insome embodiments, at least two perpendicular boundaries of the rangepattern e.g. at least one vertical line segment and at least onehorizontal line segment are identified in respective storage locations214A and 214B in store 214 as illustrated in FIG. 2H. In this example,ranges of all remaining vertical line segments are identified in storagelocations 215A-215I, and ranges of all remaining horizontal linesegments are identified in storage locations 215J-215M (wherein A≦I≦J≦M,M+2 being the total number of line segments in the range pattern). Notethat in these embodiments, stores 214 and 215 together identify thelocations and ranges of all line segments in a range pattern.

Some embodiments identify all vertical line segments in range pattern200 relative to a left boundary 200L (which is therefore a verticalreference edge) and all horizontal line segments relative to a bottomboundary 200B (which is therefore a horizontal reference edge) of rangepattern 200. Therefore, in the example illustrated in FIG. 2E, a linesegment 201L of rectangle 201 is identified as the vertical line segmentat left boundary 200L (i.e. the vertical reference edge) and anotherline segment 201B also of rectangle 201 is identified as the horizontalline segment at bottom boundary 200B (i.e. the horizontal referenceedge) of range pattern 200. Hence, two reference edges in the form ofline segments 201L and 201B are identified in respective storagelocations 214A and 214B in store 214, and ranges for all remaining linesegments in range pattern 200 are identified relative to these tworeference edges, in storage locations 215A-215M.

Note that it is not necessary for two reference edges of a range patternto belong to a single rectangle in the range pattern. Specifically,whether or not line segments identified in store 214 as being referenceedges are from a common rectangle as illustrated in FIG. 2E depends on aspecific arrangement of line segments that is unique to each rangepattern. For example, in FIG. 2I, a line segment 221L of rectangle 221is identified as the vertical line segment at left boundary 220L andanother line segment 223B of another rectangle 223 is identified as thehorizontal line segment at bottom boundary 220B of range pattern 220.Hence, in FIG. 21, the two reference edges do not belong to the samerectangle.

In addition to ranges in the vertical direction, such as width range andspacing range described above, range patterns of some embodiments alsohave ranges on dimensions in the horizontal direction, such as a lengthrange (between Lmin and Lmax) for the length of a trace 222 asillustrated in FIG. 2I. Moreover, in addition to ranges on the distancesbetween any two adjacent line segments as described above, someembodiments support the definition of ranges on distances between anytwo (or more) specified line segments in the range pattern, regardlessof whether or not the specified line segments are adjacent to oneanother. For example, the height of range pattern 220 (FIG. 2I) may havea range (Hmin, Hmax), which defines the distance between the upper edge221U of rectangle 221 and the bottom edge 223B of rectangle 223. Such arange may be either manually specified or automatically computed, and isstored in one of storage locations 215A-215M (FIG. 2H). When any rangeis manually specified, depending on the embodiment, the user may beallowed by an appropriately programmed computer to describe the range ofa line segment in a range pattern relative to any other line segmentwhich may, for example, itself be within another range identified in therange pattern.

Also depending on the embodiment, the data structure of a range patternmay contain fields to access additional stores in computer memory otherthan the above-described stores 214 for line segments at known locationsand stores 215 for ranges of remaining line segments. For example, someembodiments support the definition of one or more constraints requiredto be satisfied by any two (or more) specified line segments in therange pattern, regardless of whether or not such line segments areadjacent to one another. Such constraints are stored, in suchembodiments, in the storage locations accessed by fields 216 of the datastructure 210 illustrated in FIG. 2J. Similarly some embodiments performa scoring function which rates the numerous patterns represented by arange pattern for their effect on yield. Performance of such a scoringfunction requires, in some embodiments, a scoring formula which is heldin storage location accessed by field 217 of the data structure 210(FIG. 2J).

For the “Staircase” pattern, let the parameters a, b and c denote thespacing between the top and the middle rectangles, the spacing betweenmiddle and bottom rectangles and the width of the middle rectangle,respectively. Furthermore, let S1, S2 and W denote the minimum possiblevalue of parameters a, b and c, respectively, such that minimum widthand spacing rules for the current technology are satisfied. Then, atypical scoring function for the “Staircase” pattern is as follows:f=100−α*{(a−S1)+(b−S2)}−β*(c−W). In this equation for “f”, certainillustrative exemplary values for a and P are in the range of 1 and 2and for S1, S2 and W are in the range of 90 nm and 150 nm which arebased on values of minimum width and minimum spacing.

Additionally, or optionally, such embodiments may also store in storagelocations accessed by fields 218 in data structure 210 of FIG. 2J,optimal value(s) within corresponding range(s) that result in a localmaxima (or local minima, or median) in the score (relative to Max andMin limits in the respective ranges). While range patterns of the typedescribed above can be prepared in any manner that will be apparent tothe skilled artisan on studying this disclosure, some embodiments of theinvention perform a method of the type illustrated in FIG. 3A.Specifically, a fabrication defect in an IC chip (e.g. known to becaused by improper printing) is selected in an act 301 for use inmodeling such defects with one or more range patterns. Next, in act 302,a region of a fixed size in the IC layout around and including thedefect's location is selected (e.g. a region of 1 micron size andcentered at the defect's location is selected). Note that in manyembodiments, the just-described IC layout from which a region isselected is at a stage prior to application of any resolutionenhancement technique (RET) such as optical proximity correction (OPC).

Next in act 303 a number of test patterns are generated, by simplychanging the relative locations of line segments in the selected region.The amount of change between any two test patterns may be selected to beany amount, although one embodiment uses increments of the minimumfeature size of the fabrication process. Changes in the relativelocations of line segments are along a single dimension (e.g. width) fora set of test patterns, followed by another dimension (e.g. spacing) foranother set of test patterns and so on. Some sets of test patterns mayhave combinations of changes of multiple line segments (e.g. both widthand spacing). Numerous such test patterns are generated in act 303.

In some embodiments of act 303, several possible combinations of eachdimension that has a range are prepared into a set of test patterns,wherein each dimension is changed in a predetermined manner, e.g.changed by a predetermined increment, which may be, for example, theminimum feature size or the manufacturing grid size. If there are Nlegal values for a given dimension within its range (e.g. one value ateach multiple of the predetermined increment), and if there are Mdimensions that can be changed in a range pattern, then there could beup to T=N^(M) test patterns for a single range pattern.

As the total number T of test patterns is an exponential function of thenumber N of legal values (with the number of changeable dimensions beingtypically fixed for a given range pattern), it is necessary to minimizethe number N if the number T is to be kept sufficiently small to berealistically tested. Some embodiments deliberately generate only alimited number of test patterns, e.g. less than 1000. In several suchembodiments, an overall limit on total number of test patterns requiresusing just two values for each dimension in at least some (if not all)range patterns e.g. the two limits (max, min) of each range. In thiscase N is 2 and typically M is 5 then such embodiments build (orsimulate building of) 2⁵ i.e. 32 test patterns, for finding theappropriate dimensions of one exemplary range pattern. If there are 10range patterns in a library, then they require 320 test patterns total.

Other embodiments may support use of more test patterns, that can begenerated by use of, for example, three values for each dimension, suchas the two limits described above and a median (or mean). In this case Nis 3 and M is typically 5, so there are 35 i.e. 243 test patterns forone such range pattern. If there are 7 range patterns being used in thelibrary of such an embodiment, and if each range pattern requires 243test patterns, then there are a total of 7*243, i.e. 1701 test patterns.

Thereafter, in act 304 the results of fabrication of the test patternsare obtained, e.g. by actually fabricating an IC chip containing thetest patterns and/or by simulating the fabrication. Next, in act 305,one or more test patterns that result in fabrication defects areidentified (e.g. one or more manufacturing criteria are applied todecide whether or not the result of each test pattern is acceptable).

Once a number of patterns that result in fabrication defects areidentified, then in act 306 two such patterns that are similar to oneanother are used to define a range pattern. Similarity of two patternsmay be judged either manually by human inspection or automatically by acomputer determining that almost all (e.g. all but one) dimensions ofthe two patterns match. Thereafter, in act 307, a check is made if alldefective patterns have been represented in a range pattern and if not,then in act 308 a check is made whether a remaining defective patternfits a previously-defined range pattern. If so, then act 307 (which hasbeen just described) is repeated. If not, then similarity of thisdefective pattern relative to one of the previously-defined rangepatterns is determined, and if there is a similarity then the rangepattern is modified in act 310, followed by returning to act 307. Ifthere is no similarity, then act 311 is performed to create a new rangepattern that covers this defective pattern followed by returning to act307. In act 307, if there are no more defective patterns left, then act312 is performed to check if all defects in the IC chip have beenmodeled by one or more range patterns and if not act 301 is repeated.

In some embodiments, instead of (or in addition to) performing thejust-described method of FIG. 3A, a human's experience with ICfabrication is used to receive from the human data required to define arange pattern, as illustrated in FIG. 3B. Specifically, in act 321, thelocation of an edge of a rectangle at a left boundary of the pattern isreceived, followed by receiving the location of a rectangle's edge at abottom boundary of the pattern. Next, act 322 receives a range (i.e.minimum limit and maximum limit) for the location of an edge, relativeto any previously-received edge. Each of acts 321 and 322 may berepeated as often as necessary, until the range pattern is fullydefined. In some embodiments, as the input is received a graphicaldisplay is updated to show the edges of the range pattern that have beenreceived so far. Note that in such a display, all edges may be shown atminimum distances in their respective ranges, with a label at each edgeidentifying its range (e.g. as shown in FIG. 2E). Moreover, depending onthe embodiment, additional data may be received from such a human, e.g.optimal values and/or constraints may be received in respective acts 323and 324 as illustrated in FIG. 3B. Note also that such acts can beperformed in any order relative to one another.

Once a memory contains one or more range patterns of the type describedabove, a computer containing such memory (or with access to such memory)can be programmed to use the range pattern(s) to avoid one or morefabrication issue(s) as illustrated in FIG. 3C. Specifically, an IClayout is designed in act 331 in the normal manner, followed by such acomputer using the range pattern(s) to identify in act 332 any locationsin the just-designed IC layout that match the range pattern(s). If thereis no match in act 332, then analysis and extraction and/or physicalverification and/or resolution enhancement are performed in act 333 inthe normal manner, followed by mask data preparation and IC fabricationin act 334. For more details, see FIG. 14B and its description below. Ifthere are one or more matches in act 332, then a region in the layoutthat contains the matching location is re-designed, e.g. by changing theresources available to a layout router followed by invoking the layoutrouter.

Any prior art method for rip-up and re-route may be used, depending onthe embodiment, to correct the IC layout. As many embodiments in thecurrent patent application are primarily directed to novelty related tospecification of range patterns and detection of matching regions in alayout, details of correction are not critical to practicing suchembodiments of the invention. In some embodiments of the invention,regions requiring re-design are modified using simple techniques such aswire-spreading or wire-widening while other embodiments use more complexrip-up and re-route strategies, and still other embodiments usecombinations thereof. For instance, in case of a staircase pattern, someembodiments initially attempt to widen the central line (i.e. middlewire) beyond 150 nm or to increase the spacing between the central lineand the top and bottom lines. When such initial attempts fail, theseembodiments rip up the entire staircase pattern and new routing forthese wires is generated through a place and route tool. To prevent apreviously-generated pattern from being re-generated by the place androute tool, new DRC rules are imposed on the tool. The new DRC rules areautomatically generated in some embodiments from the range pattern (e.g.DRC rules are created as complements of conditions present in the rangepattern) and these new DRC rules are enforced during the new routing(i.e. redesign) in addition to the DRC rules normally used in the placeand route tool.

Note that the re-design being done in some embodiments is incremental,i.e. the whole layout is not changed and instead just a small amount of(1) rip up and re-route and/or (2) wire spreading and/or widening isdone, typically in a region of a predetermined size that surrounds thelayout location which has been identified as being defective by use of arange pattern. For example, when the staircase pattern shown in FIG. 1Dis re-designed, a newly-generated pattern is shown in FIG. 4A with thespacing S and the overlap O being much larger than before. Accordingly,the result of fabrication as shown in FIG. 4B avoids the pinching effectshown in FIG. 1F. Note that after such re-designs are done for severaldefective locations (in some embodiments for all defective locations),act 332 is repeated to identify any defects that may have remained (e.g.if re-design was ineffective) or may have newly arisen (due to there-design).

In one illustrative embodiment, the memory of a computer is loaded witha range pattern library that contains several range pattern format fileswhich specify different range patterns. A typical range pattern formatfile contains the following data: (1) Name of the range pattern: validnames can consist of letters and numbers, but may not start with anumber; the names are case sensitive. (e.g. Name=Rocket;) (2) In whichrouting direction can the range pattern be found: valid routingdirection can be hor, vert or both. (e.g. Dir=hor;) (3) Number ofrectangles in the range pattern: valid number of rectangles is apositive integer. (e.g. RectNum=3;); note that edges of rectangle 1 arerepresented as Ri.l (left edge), Ri.r (right edge), Ri.b (bottom edge)or Ri.t (top edge) ( ); (4) Left edges of the rectangles which are onthe left boundary of the range pattern. (e.g. LeftBry R0.1, R2.1;) (5)Bottom edges of the rectangles which are on the bottom boundary of therange pattern. (e.g. BottomBry R2.b;); (6) Rectangle edges at the rangepattern boundaries which need to be checked to make sure the rectanglescannot extend out of the boundaries(e.g. StrictBryCheck R0.t, R2.b; orLooseBryCheck R1.r;); note that the functions StrictBryCheck andLooseBryCheck denote two different types of rectangle boundary checks asdiscussed in the next paragraph; (7) Ranges on the distances between therectangle edges. (e.g. R0.t−R0.b is (90,150)[90];); note that exemplarydistance between R0.b and R0.t is between 90 and 150 with optimal value90.

Two types of checks can be performed prior to identifyingrange-pattern-matched locations of a layout as hotspots, whereindigitized-data at the boundary of the layout block is checked to ensurethat no material is present, either all around the boundary(“StrictBryCheck”) or at least at one location on one or more sides ofthe boundary (“LooseBryCheck”).

As an example, a user's specification for the Staircase pattern asillustrated in FIG. 1 D is given below:

Name=Staircase;

Dir=hor;

RectNum=3;

LeftBry R0.1;

BottomBry R2.b;

R1.l−R0.l is (10, 50);

R0.r>Rl.l;

R1.r>R0.r;

Rl.r−R1.l is (200, 500);

R1.r>R2.l;

R0.r−R2.l≦=50;

R2.t−R2.b is (90, 150)[90];

R0.t−R0.b is (90, 150)[90];

R1.b−R2.t is (90, 150)[90];

R1.b−R2.t is (90, 150)[90];

R1.t−R1.b is (90, 150)[90];

R0.b−R1.t is (90, 150)[90];

In some embodiments of the invention, the range patterns as well as thelayout are sliced as illustrated in FIGS. 5A-5E, and it is the slices(e.g. slices S0-S4 as illustrated in FIG. 5A) which have resulted fromslicing that are compared in act 332 (FIG. 3C). Each slice S1 of a rangepattern is oriented parallel to another slice SJ of the range pattern.Moreover, slices that are adjacent to one another are not equal, in thesense that the presence or absence of material in the layout is atdifferent locations in different slices. Within a given slice SI, in thelateral direction (i.e. in the direction perpendicular to the slicingdirection), material is at the same location in the slice S1, althoughin the longitudinal direction of the slice, the material can be atdifferent locations within the slice SI.

Each slice SI in a sliced version of a pattern typically includes one ormore regions wherein material is present in the layout, and/or one ormore regions wherein material is absent in the layout (the regions arehereinafter called “fragments”). Specifically, each slice SI may containone or more fragments FIJ, wherein J identifies the location of thefragment within the slice SI (relative to another fragment within thesame slice). For example, slice S2 is illustrated in FIG. 5A ascontaining three fragments F20, F21 and F22, wherein material is presentin fragment F21 while being absent in the two fragments F20 and F22 thatare adjacent to fragment F21. As two additional examples shown in FIG.5A, slice S2 is adjacent to two slices S1 and S3 that respectivelyconsist of the two fragments F10 and F30 (wherein material is absent inthis example). Moreover, slices S1 and S3 are respectively adjacent toslices S0 and S4 that respectively contain the pairs of fragments (F00,F01) and (F40, F41).

A specific direction in which a range pattern is sliced (such as thehorizontal direction in FIG. 5A) can be different for different rangepatterns in a library. In the example illustrated in FIG. 5A, thedirection of slicing is in the longitudinal direction of the traces F00,F21 and F41, which happens to be horizontal as it is the longitudinaldirection of the traces. In this example, each slice has the width of atrace and/or the width of spacing between adjacent traces and hence asingle sliced version is adequate to fully represent the range patternof FIG. 5A.

Note, however, that more than one sliced version may be required torepresent the given range pattern, e.g. if in the given range patternthe ranges on multiple dimensions are such that the given range patterncannot be represented by a single sliced version. When slicing suchrange patterns, a specific slicing direction is selected in someembodiments to minimize the number of multiple sliced versions that maybe required to represent a given range pattern. An example of a rangepattern that requires multiple sliced versions, is the door patternshown in FIG. 5B which requires four sliced versions illustrated inFIGS. 5C-5F.

Specifically, the door pattern of FIG. 5B includes two pads 501 and 502whose widths (in the horizontal direction) may in some cases overlap oneanother when viewed in the vertical direction (as shown in FIGS. 5D-5F),but not overlap in other cases (as shown in FIG. 5C), depending on thevalues in the respective width ranges. Specifically, in some cases theright side of pad 501 may be to the right of the left side of pad 502 inwhich case there is an overlap on the right side as shown in FIG. 5D,and alternatively the right side of pad 501 may be to the left of theleft side of pad 502 in which case there is no overlap as shown in FIG.5C. The just-described two cases are covered by use of two slicedversions illustrated in FIGS. 5C and 5D. A similar situation arises ifthe width of pad 503 is also variable in a specified range withoverlapping pattern shown in FIG. 5E. FIG. 5F shows overlap on bothsides of pad 501. Therefore four sliced versions are required toadequately represent the range pattern illustrated in FIG. 5B.

Note that a “mountain” range pattern illustrated in FIG. 5G requiresonly one sliced version when sliced in the longitudinal direction of thetraces, although multiple sliced versions (not shown) are required ifsliced laterally. Hence, to minimize the amount of memory required tohold sliced versions of range patterns and to minimize the amount ofcomputation when matching a sliced version to a layout, many embodimentsof the invention slice a range pattern in each of lateral direction andthe longitudinal direction (relative to traces) and then selectwhichever slicing direction generates the smallest number of slicedversions. In such embodiments, for the mountain range patternillustrated in FIG. 5E, the longitudinal direction is selected as theslicing direction and the resulting sliced version is stored in computermemory (FIG. 2D), for use in matching.

Some embodiments of the invention perform a method illustrated in FIG.5H to identify portions of a newly-created layout that match one or morerange patterns of the type described above, so that such portions may bere-designed to avoid fabrication issues. Specifically, as illustrated inFIG. 5F, all range patterns in a library are sliced as per act 511.During this act, one or more overall dimensions of each sliced versionof each range pattern are also computed. Examples of overall dimensionsinclude the minimum and maximum length as well as the minimum andmaximum width of the range pattern. Then, in act 512, a sliced versionis selected for comparison to patterns in the layout. Next, in act 513,a block of the layout is selected, for example to have a length same asthe minimum length, of the selected sliced version of the range pattern.Thereafter, in act 514, the selected block of the layout is sliced, in amanner similar or identical to slicing of a range pattern as describedabove in reference to FIGS. 5A-5E.

Next, in act 515, a computer which implements the method of FIG. 5Hcompares the sequence of width ranges of the selected pattern's sliceswith a sequence of widths of the layout block's slices. Thereafter, inact 516, the computer checks if the width range sequence matches anywidth sequence in the block. If there is no match, the computer ofseveral embodiments goes to act 519 to check if all the blocks have beencompared to the currently selected pattern and if not compared then thecomputer returns to act 513 (described above). If all the blocks havebeen compared, the computer goes to act 520 and checks if all of thesliced versions for a currently-selected pattern have been compared, andif not the computer goes to act 512 (described above). In act 520, ifall sliced versions have been checked, the computer goes to act 511(described above). An alternative embodiment improves the speed ofperformance (and run time efficiency) by performing the acts 511-515 notin the sequence shown in FIG. 5H but in the sequence shown in FIG. 5Iwherein acts 511, 513 and 514 are performed prior to act 512 (i.e. inthis embodiment act 512 follows act 514). Note that the specific orderof acts can be different in different embodiments, depending ontradeoffs such as memory and/or processing speed.

In act 516, if there is a match between the width range sequence and anywidth sequence in the block, then the “yes” branch is taken to act 517.Hence, act 517 is entered when the slices in the block are similar toslices in the range pattern, and therefore in act 517 a slice-by-slicecomparison is performed, to confirm that each of the fragments within aslice of the layout block match corresponding fragments in thecorresponding slices in the range pattern. Specifically, in act 517 thecomputer of many embodiments is programmed to compare the sequence oflengths of the fragments in each layout slice in the block with therespective sequence of length ranges of each slice's fragments in therange pattern. Then, in act 518, the computer checks if any of thelayout fragments' length falls outside of the respective fragment lengthrange in the pattern, and if so then there is no match and the “yes”branch is taken to act 519 (described above).

In act 518, if the slice-by-slice comparison finds that every fragmentof the layout matches the corresponding range in the pattern, then the“no” branch is taken to act 522. Note that act 522 is an optional act inwhich one or more constraints (of the type described above) are appliedin some embodiments of the computer. If the constraints are satisfied inact 522, then act 523 is performed to mark the block as a match, andthereafter the computer returns to act 519 (described above). If theconstraints are not satisfied in act 522, then the computer goesdirectly to act 519. Moreover, if act 522 is not performed, then thecomputer goes directly to act 523 to mark the block as a match and thengoes to act 519 from act 523. Moreover, if the “yes” branch is takenfrom act 518, then the computer goes directly to act 519.

The above-described acts illustrated in FIG. 5H are performedhierarchically, in some embodiments of the invention. Specifically, themethod of FIG. 5H is first performed (as illustrated in FIG. 6A) ondigitized data of the range pattern and of the layout block generated byusing a grid of a predetermined size (“coarse grid”) that is selected tobe sufficiently large to identify potential matches (including one ormore false matches as well as true matches). Next, the method of FIG. 5His repeated on the potential matches (as illustrated in FIG. 6F) usingdata obtained from digitization with a grid (“fine grid”) that is finerthan the coarse grid. The fine grid is designed to have a sufficientlysmall size to remove false matches from among potential matchesidentified by use of the coarse grid. For this reason, hierarchicalmatching refers to use of the two grids of different sizes as describedherein.

Before outputting the matched locations at the end of applying the finegrid (e.g. by saving to computer memory or to non-volatile storagemedium, such as a hard disk) one or more constraints on relativelocations of line segments in the range pattern are also checked, asdescribed above in reference to optional act 522. In two examples ofchecks performed prior to identifying the matched locations of a layoutas hotspots, digitized data at the boundary of the layout block ischecked to ensure that no material is present, either all around theboundary (“strict check”) or at least at one location on one or moresides of the boundary (“loose check”). Several embodiments solicit userinput to enable/disable checks and/or to obtain data used in suchboundary checks. A third example of such checks is illustrated by anoverlap constraint Omax on the boundaries of two traces 221 and 223between which is located a middle trace 222 that can get pinched due tooverlap, as described above in reference to FIG. 2I.

FIG. 6A illustrates, in a flow chart, matching of a block of a layout toa library of range patterns in some embodiments of the invention using acoarse grid. Initially, a layout that has been output by a routing tool,such as layout 601 is provided as input to an act 602. In act 602, awindow of a predetermined size and shape, such as a square window ofwidth w is initialized, at a predetermined location relative to thelayout, to select a portion of the layout for comparison with slicedversions of range patterns in a library 605 (located in computermemory). In an illustrative example, the window is selected to be 1000times grid size, wherein a layout is of size 2 mm×2 mm is digitizedusing a coarse grid of size (i.e. pitch) selected to be 50 nm (asdiscussed below), so the window is selected to be 50 μm×50 μm.

In some embodiments, such a window is aligned to the left side of thelayout, and depending on the embodiment, the window can be located atthe top left corner or the bottom left corner of the IC layout. Notethat the window may be alternatively positioned at any location in thelayout, such as the top right corner or the bottom right corner of theIC layout. The window is eventually panned across the IC layout, tocover the entire layout, by repeating the acts described below. Althougha specific size, a specific initial location of the window and aspecific movement of the window across the layout are described hereinfor illustration, other embodiments use other sizes, initial positionsand movements.

Next, in act 603, presence or absence of material 610 (FIG. 6B) in theportion of layout 601 that is located within the current window is usedto generate a matrix for the layout, by representing the presence by abinary value “1”, and representing the absence as a binary value “0”.Digitization of the layout into a matrix is performed in someembodiments, using a grid 611 formed by a number of vertical linesspaced apart by distance 612 (FIG. 6B) overlaid by a number ofhorizontal lines spaced apart by distance 613. Intersections of the gridwherein the material is present, e.g. at 615I and 615J (FIG. 6C) arerepresented by the value “1” and other intersections of the grid wherematerial is absent, e.g. at 614A and 614Z are represented by the value“0”. The horizontal and vertical separation distances 612 and 613 of thelines in grid 611 are selected to be identical to one another (called“grid size” or pitch) and the value thereof is greater than a minimumlimit. The just-identified minimum limit is selected in some embodimentsto be manufacturing grid of a process to be used in fabricating theintegrated circuit. Hence, the grid size is selected to be e.g. greaterthan 5 nanometers.

A larger grid size (than the 50 nm size described above for a coarsegrid) is chosen in some embodiments to improve runtime efficiency.However, the larger the grid size (see distance 612, 613 in FIG. 6B) themore likely that different features appear to be the same, from loss ofresolution due to digitization. Therefore, digitization results in falsepositives in potential matches 609 (output by act 604), and the numberof false positives in turn depends on the grid size. For this reason, agrid size for grid 611 (FIG. 6B) is selected, in most embodiments, to beat least smaller than a minimum feature size, which is typicallyspecified by a fabrication facility (such as TSMC), e.g. in design rulecheck (DRC) rules. In several embodiments, to reduce the number of falsepositives to a sufficiently small number, the grid size (or pitch) isselected to be smaller than half of the minimum feature size. Forexample, in a 65 nanometer design, if the minimum feature size is 90nanometers, grid 611 is selected to have a grid size of 45 nanometers.

In the example where a coarse grid size of 45 nm is selected, three gridpoints are located at the following distances from the bottom leftcorner of the window, i.e. 45 nm*2=90 nm, 45 nm*3=135 nm, and 45nm*4=180 nm. So any feature that is of dimension 90 nm to 135 nm appearsonly as two grid points on the 45 nm grid. Any feature that is ofdimension 136 nm to 180 nm appears only as three grid points on the 45nm grid. If a range pattern in library 605 specifies a range whichincludes a dimension between 90 nm and 150 nm, and if the resolutionjumps from 135 nm to 180 nm, then pattern matching on a layout matrixobtained by digitizing (as per act 604 in FIG. 6A) identifies aspotential matches 609 several features which are not truly hotspots buthappen to have dimensions greater than 150 nm and less than 180 nm (inaddition to truly hotspot features having dimensions from 90 nm to 150nm).

In several embodiments of the invention, one or more such falsepositives are removed from potential matches 609, by repeating thematching in regions of the layout 601 containing the potential matches609, using a second grid of a smaller grid size (as per FIG. 6F;described below) which maintains sufficient resolution in the digitizeddata to distinguish between a shape that is at 130 nm dimension andanother that is at 160 nm dimension. Note that in the followingdescription, the grid (and its size/pitch) used in act 603 in FIG. 6A isreferred to as a “coarse grid” (and “coarse grid size”), whereas thecorresponding grid (and its size/pitch) used in act 623 in FIG. 6F isreferred to as a “fine grid” (and “fine grid size”).

Implementation of act 604 (FIG. 6A) to match a submatrix in the layoutmatrix of window size (output by act 603) to a range pattern in library605, depends on the specific embodiment. Some embodiments performmatching in act 604 by implementing a method of the type illustrated inFIG. 5H (discussed above). Note, however, that any matching algorithmwell known to a skilled artisan may be used to identify within thelayout matrix, each submatrix that matches a pattern covered by aselected range pattern from library 605. Such a matching algorithm isperformed repeatedly in act 604, for each range pattern in library 605.

Once all potential matches to all range patterns within the currentwindow are identified in act 605, the computer performs act 606 to checkif the entire layout has been panned by the above-described window(which was used to digitize a region of the layout in act 603), and ifnot then the computer proceeds to act 608 to identify a new window'scoordinates (e.g. by panning the window), and thereafter returns to act603 (described above). In act 606, if the entire layout has beencovered, the computer proceeds to act 607 to verify potential matches609 (to screen out one or more false positives) by performing the actsshown in FIG. 6F (described below).

In some embodiments of the invention, in act 608, the window is pannedhorizontally in incremental movements that maintain a horizontal overlap618 between a current window 616 (shown by a solid line in FIG. 6D) andthe next window 617 (shown by a dashed line in FIG. 6D). Such an overlap618 is selected to be sufficiently large to ensure that a pattern in thelayout 601 (FIG. 6A) that spans from within the window 616 to within thewindow 617 is not missed (i.e. the location is identified as matched toa library pattern in one of the two windows). Therefore, in someembodiments, a maximum dimension of a range pattern in library 605 isdetermined (e.g. prior to act 602 in FIG. 6A) and this value is used toset the value of horizontal overlap 618. For example, if the maximumlength of a range pattern is ml, the overlap 618 is set to m1+1 in someembodiments.

After panning the window in the horizontal direction in this manneracross the entire length of the IC layout 601, the horizontal panning ofthe window is repeated after moving the window vertically up by adistance which is selected to maintain an overlap distance 619 (FIG. 6E)in the vertical direction. Hence, in a manner similar to that describedabove for the horizontal overlap, if the maximum height of a rangepattern is m2, the vertical overlap distance 619 is set to m2+1 in someembodiments.

Although in some embodiments (“horizontal-scanning embodiments”), thecomputer is programmed to first move the window horizontally, and ontraversing through the length of the layout then to move the window upone step in the vertical direction and repeat the horizontal movement,certain embodiments (“vertical-scanning embodiments”) of the computerperform such movements in the inverse order, i.e. move the windowvertically first across the entire layout followed by one step in thehorizontal direction followed by repeating the vertical movement. Stillother embodiments may perform such window movement in any order as longas all the window regions that are explored in a horizontal-scanningembodiment (or a vertical-scanning embodiment) are also explored in suchother embodiments. Hence, the specific order of movement is not acritical aspect of most embodiments

In some embodiments of the invention, the computer is programmed toimplement a lower level of hierarchical matching, by performing a methodof the type illustrated in FIG. 6F. Specifically, in act 621, thecomputer inputs potential matches including false positives that weregenerated in the method of FIG. 6A, from nonvolatile memory or otherstorage media in which potential matches 609 are stored by the top levelof hierarchical matching. Next, in act 622, the computer checks if ithas finished checking all of the matches in set 609 of potentialmatches. If not finished, then the computer goes to act 623 andgenerates the layout matrix using a fine grid size as discussed above,for a potential match.

Next, in act 624, the computer again implements a matching algorithm ofthe type described above, for example in reference to FIG. 5F, althoughthe comparison is now done using data obtained by digitizing the layoutusing the fine grid. In act 624, it is not necessary to compare thelayout matrix with each and every range pattern in the library. Insteada range pattern that matched in act 604 to the layout, is stored inmemory with each potential match 609, and in act 624 each potentialmatch is compared to its corresponding range pattern from coarse levelmatching (described above in reference to FIG. 6A).

After act 624 is performed, the computer returns to act 622 (describedabove). In act 622 if all potential matches identified in set 609 havebeen checked at the fine level, then the computer goes to act 625. Inact 625, the computer outputs into memory as hotspots (which need to bere-routed), all locations in the layout that match a range pattern atthe fine level (in act 624), assuming constraints (if any specified) aremet, as described elsewhere herein.

Some embodiments of the invention apply the method of FIG. 5H to awindow of digitized data, by using blocks of varying sizes asillustrated in FIG. 6G. In some embodiments, a block (of the type shownin FIG. 7) is selected to have a width which is same as the window'swidth, and to initially have a height same as the minimum height minR ofa range pattern which is being compared to the layout. The block'sheight is varied between minR Oust described) and maxR which is themaximum height of the range pattern in increments of one row, andfurthermore the block is moved in the vertical direction, to span theentire height of the window. In some embodiments, a block which has theheight minr is incremented one row at a time until the maximum heightmaxR is reached, followed by moving the block up by one row, followed bydecrementing one row at a time until the minimum height minR is againreached and this process is repeated. In some embodiments, only adiscrete number of blocks between minR and maxR are enumerated, and theenumeration can be done in any order, such as from maxR to minR or viceversa. One such embodiment shortens each subsequent block (in thesequence of enumeration) whereas another such embodiment elongates eachsubsequent block.

In an example illustrated in FIG. 6G, block 631 is incremented by onerow to obtain block 632, and thereafter block 632 is further incrementedby one row to obtain block 633 which has the maximum height maxR.Thereafter, once the height maxR has been reached, block 633 is moved upby one row to obtain block 634. Next, the block 634 which is of maximumheight maxr is decremented in size by one row to obtain block 635,followed by decrementing once again to obtain block 636. Thereafter,block 636 is moved up by one row to obtain block 637. Block 637 isthereafter incremented by one row to obtain block 638 which in turn isincremented once again to obtain block 639, followed by moving the blockup by one row to obtain block 643 which has the maximum height maxr.

Hence, a worm-like movement and re-sizing of the block is performed tospan the entire window, when comparing the layout to the range patternin some embodiments. During such movement, the digitizing of each newblock reuses most of the work done in digitizing a previous block.Specifically, during the worm-like movement, in each pair of adjacentblocks, only one row is changed, either at the top or at the bottom ofthe block and therefore most of the work in digitizing the remainingrows is reused between the two adjacent blocks. For example, in FIG. 7,when bottom row 777 is dropped, and a new top row (not shown) is added,the boundaries of slices 700-712 (shown by dashed lines) may remain thesame, although within each slice the boundaries of fragments therein may(or may not) change.

In some embodiments of the invention, a sequence of bits that representthe presence or absence of matter in an IC layout is encoded into asingle value for each slice as follows. Specifically, the computerencodes each slice by appending a bit “1” as the most significant bit inthe sequence, to distinguish between the sequence “01” (which denotesthe absence of matter and the very bottom followed by presence ofmatter) and the sequence “1” (which denotes the presence of matter atthe very bottom). For example, a sequence for slice 551 (FIG. 5E) whichcontains a single fragment F00 of binary value 1 when prepended withanother binary value 1, result in the encoded binary value “11”, whichhas the decimal value 3.

Similarly, a sequence for slice 552 (FIG. 5E) which includes fragmentsF10 and F11 of respective binary values 0 and 1, when prepended with thebinary value 1 results in the encoded binary value “101” which has thedecimal value 5. The just-described encoded binary value for slice 552is obtained as follows: 1 (msb), 0 (F10) and 1(F11). Furthermore, asequence for slice 553 which includes the fragments F20, F21 and F22 ofthe respective binary values 1, 0 and 1 when prepended with the binaryvalue 1 results in the encoded binary value “1101”, which has thedecimal value 13. Slices 554 and 555 when similarly encoded have alsothe decimal values 5 and 3, similar to slices 552 and 551 describedabove. Therefore, the mountain pattern illustrated in FIG. 5G is encodedinto the one dimensional string 3, 5, 13, 5, 3.

The above-described encoding method for each slice is applied not onlyto a range pattern as described above but also to a layout block of thetype illustrated in FIG. 7. Specifically, slices 700-712 of FIG. 7 whenencoded have the decimal values 2, 10, 10, 2, 3, 5, 13, 5, 3, 2, 10, 10,2. After such encoding, when the just-described one dimensional stringof decimal values for the block in FIG. 7 is compared with acorresponding string of decimal values for the range pattern illustratedin FIG. 5E, notice that there is an exact match starting with slice 704.As described elsewhere herein, such comparison is performed in someembodiments of an appropriately programmed computer, by use of any exactstring matching method. An alternative encoding scheme for a slice ofsome embodiments represents a fragment as a 1 or 0 in the mannerdescribed above, and then counts the number of 1 s in the slice (andthis number is denoted as “n”). In this alternative encoding scheme, ifthe first fragment of slice is 1, this entire slice is represented as +n(i.e. a positive number), else this slice is represented as −n (i.e. asa negative number). This alternative encoding scheme also replaces eachslice with a number (see acts 1113 in FIG. 11B and FIG. 18, see act 1133in FIG. 11D, see act 1307 in FIG. 13A and see act 1309 in FIG. 19).Hence, in the alternative encoding scheme as well, both the rangepattern and the layout are represented as a string of numbers andthereafter a matching of the range pattern to the layout is performed asdescribed above.

In some embodiments of the invention, library 605 of range patternsinitially contains data on each range pattern in a format as provided bythe user, e.g. relative positions of edges of rectangles in the rangepattern, such as R1.1 (left edge of first rectangle), R1.r (right edgeof first rectangle), R1.b (bottom edge of first rectangle) and R1.t (topedge of first rectangle). Such a library of range pattern is processedin such embodiments as illustrated by the method in FIG. 8A.Specifically, in act 801, the computer is programmed to select a rangepattern from library 605. Next, in act 802, the computer sets up anadjacency matrix which identifies the distance (or range) betweenparallel edges of the selected range pattern, based on the user inputdata (described above). For example, if a range pattern that is selectedin act 801 is the staircase pattern illustrated in FIG. 2I, then in act802 the computer sets up a square matrix of size 6 to identify thedistances (or ranges) between all horizontal edges, because there aresix horizontal edges whose distance from one another is specified in therange pattern in library 605. Note that an adjacency matrix contains asits elements, the dimensions (or limits thereon) of a range pattern in aspecific direction, such as horizontal direction or vertical direction.

Examples of the adjacency matrices for horizontal distances and verticaldistances in the staircase range pattern are illustrated in FIGS. 8C and8D respectively. An element [1][2] in such an adjacency matrix (i.e.located at row 1, column 2) in FIG. 8C defines a distance (or range)between bottom edge R1.b (edge 223B in FIG. 2I) and top edge R1.t (edge223T in FIG. 2I), i.e. the width (or width range) of rectangle 223, e.g.the range (90, 150) nanometers. An element of the adjacency matrix thatis at a complementary location relative to another element in the matrixtypically has values that are opposite. For example, an element in theadjacency matrix of FIG. 8C at the complementary location [2][1] has therange (−150, −90), which is negation of the range(90, 150) for element[1][2]. Such opposite ranges are required to ensure consistency. Eachelement in the adjacency matrix of several embodiments has a pair ofvalues representing the minimum and maximum limits of the range asillustrated in FIG. 8C. However, in some embodiments, each elementfurther includes (in addition to the two limits of the range), anoptimal value for use in scoring (and prioritizing) a hotspot in thelayout that matches the range pattern. In such embodiments, each elementin the matrix has three values: minimum, maximum and optimal.

Next, in act 803, the computer automatically computes one or more rangesbetween edges of the selected range pattern which are uninitialized.Typically, a user may not initialize ranges between non-adjacent edges,such as a range on an overall dimension of the range pattern. In theexample shown in FIG. 2I, while a range between edges 222B and 222T isinitialized in act 802, the range between edges 223B and 222B, and therange between edges 223B and 222T is computed in act 803. The rangebetween edges 223B and 222B is computed in some embodiments as the sumof the width range and the spacing range. During such computation, theminimum limits of two (or more) ranges are added to obtained the minimumlimit of a combined range, and the maximum limits of the ranges areadded to obtain the maximum limit of the combined range. For example, ifa range for trace width in range pattern 220 has been specified to be(90 nm, 90 nm) and if the spacing between adjacent traces is specifiedto be (90 nm, 130 nm), then the range (Hmin, Hmax) on the overall heightof range pattern 220 is automatically computed by the computer to be(450 nm, 530 nm).

In act 803 of several embodiments, the computer computes a range foreach relative distance between every pair of non-adjacent edges in everyrange pattern in a library to be used for detecting hotspots. After suchcomputation, some embodiments of the computer automatically correct (ifappropriate) a previously initialized value for a range, if such valuediffers from a corresponding value obtained by such computation. Thevalues may differ, for example, due to user error in inputting the data.Note that such errors are detected only in those embodiments whichcompute such ranges even if already initialized. Thereafter, in act 804,the computer automatically slices the selected range pattern, and usesthe adjacency matrix to enumerate all sliced versions of the rangepattern. A range pattern may be sliced by the computer in any direction,e.g. in the longitudinal direction of traces, depending on theembodiment. In some embodiments, the direction of slicing is selected byperforming a method described below in reference to FIG. 8D. Note thatacts 801-804 in FIG. 8A are merely an illustrative implementation of act511 in FIG. 5H which may be implemented differently in otherembodiments. Each range pattern's sliced version(s) that have beenenumerated are stored in computer memory, e.g. in a library, for futureuse in comparison with an IC layout. An example of a data structure forstoring a range pattern's sliced version is illustrated in FIG. 8B.

The sliced pattern data structure of the example illustrated in FIG. 8Bis as follows: Integer sliceNum (Number of slices—see field 811 in FIG.8B); RangeType *sliceRange (Pointer to Range information of eachslice—see fields 812A-812N); Integer *sval; (Pointer to encoded value ofeach slice—see fields 813A-813N); Integer *fnum; (Pointer to number offragments in each slice—see fields 814A-814N); Integer ** fVal; (Pointerto an array of values of each fragment in each slice—see fields815A-815N); and RangeType **fRanges; (Pointer to array of rangeinformation of each fragment—see fields 816A-816N). Note that RangeTypeis a datastructure with 3 integer fields: min, max and opt.

Note that act 804 determines the slice widths and fragment lengths whichinformation is subsequently used, as described above in reference toacts 515 and 517 described above. Next, in act 805, the computercompares slices in each sliced version of a selected range pattern toslices in the layout, to find one or more locations in the layout thatare susceptible to fabrication issues. Thereafter, the computer checksin act 806 to see if all of the range patterns in the library have beensliced and used in comparison with the layout. If so, the computerproceeds to act 807 to change routing in those locations in the layoutthat have been flagged as hot spots in act 805. In act 806, if all ofthe range patterns in the library 605 have not yet been processed, thenthe computer returns to act 801 (described above).

In some embodiments of the invention, acts 802 and 803 and a modifiedversion of act 804 of FIG. 8A are performed twice, once for slicing inthe horizontal direction and another time for slicing in the verticaldirection, as illustrated by acts 802A, 803A and 804A for verticalslicing, and acts 802B, 803B and 804B in FIG. 8D. Note that act 804 ofFIG. 8A is modified in FIG. 8E by counting the number of slicedversions, instead of enumerating them in acts 804A and 804B. Thereafter,in act 811, the computer is programmed to check if the number of slicedversions in the vertical direction is less than the number of slicedversions in the horizontal direction. If so, the computer goes to act812A to identify all of the vertically sliced versions that are neededto adequately represent the range pattern (as described above inreference to FIGS. 5C and 5D), and also to identify individual slicesand fragments and their ranges in each of the sliced versions. If in act811, the answer is no, then the computer proceeds to act 812B, which issimilar to act 812A except for identification of horizontally slicedversions and the slices therein. Therefore, the method of FIG. 8Eminimizes the number of sliced versions of a range pattern that arematched to a layout.

In several embodiments of the invention, acts 803A and 803B areimplemented by performance of a method in an appropriately programmedcomputer to automatically compute uninitialized ranges between edges ofthe range pattern, in the respective directions. Specifically, at thebeginning of this method, all ranges that are uninitialized (by theuser) in the adjacency matrix are automatically initialized to (−∞),+∞), followed by automatically checking for the smallest upper bound andthe largest lower bound on each range. Note that in FIGS. 8C and 8D(described below) MN denotes −∞ and MX denotes +∞. Some embodiments usea graph traversal method on a graph in which each node represents anedge in the range pattern, and each arc in the graph represents adistance between two edges in the range pattern. Note that an adjacencymatrix represents such a graph, wherein presence of a value at location[i]b] in the matrix represents an arc in the graph. Each arc in thegraph is associated with a weight, which may be one of the limits of therange, either the minimum limit or the maximum limit.

Note that the weights for such a graph are based on the ranges that theuser provides, and any range that is not provided by the user isinitialized to (−infinity, +infinity), and this pair of initializedvalues is overwritten with a corresponding pair computed using the FloydWarshal algorithm as described below.

The Floyd Warshall algorithm is used in some embodiments of a computerthat is programmed to perform acts illustrated in FIG. 9A to find theshortest path between any two nodes in the graph (i.e. edges of therange pattern). Specifically, two graphs are traversed by use of theFloyd Warshall algorithm in FIG. 9A, one graph contains maximum limitsand is traversed in act 904 and the other graph contains minimum limitsand is traversed in act 906 as discussed next.

In act 904, the computer checks to see if there is a path (formed ofarcs of the graph) between nodes [I] and [J], via a node [K] whosemaximum value is less than the maximum value of a direct path betweennodes [I] and [J]. If so, the computer goes to act 905 and replaces themaximum value for the direct path between nodes [I] and [J], with thenewly-found value maximum value via node [K]. In act 904, if the answeris no, the computer proceeds to act 906. The computer also enters act906, on completion of act 905. Note that some embodiments perform an act(not shown) prior to performance of act 904, wherein the computer checksto make sure that the value of I is not equal to the value of J, and thevalue of I is not equal to the value of K, and the value of J is notequal to the value of K, thereby to avoid diagonal elements of theadjacency matrix (which are null and should remain null).

In act 906, the computer checks to see if there is a path between nodes[I] and [J] via node [K] is whose minimum value is greater than theminimum value of a direct path between nodes [I] and [J], and if so thecomputer goes to act 907 to update the minimum value, and otherwiseproceeds to act 908. The computer also proceeds to act 908 aftercompletion of act 907. In act 908 the computer checks if the value of Jhas run through the number of rows in the adjacency matrix, and if notreturns to act 903 which increments J and proceeds to act 904. In asimilar manner, the computer loops over I in acts 909 and 902, and overK in acts 910 and 901. Performance of such a method on the adjacencymatrix in FIG. 8C, yields the matrix illustrated in FIG. 9B.

A computer-implemented method of the type illustrated in FIG. 9A (withor without use of the Floyd Warshall algorithm) is useful when multiplepotential paths exist between any two parallel edges of a range pattern(e.g. between the topmost edge and bottommost edge of the rangepattern). Multiple paths between two graph nodes (i.e. edges in a rangepattern) are common in complex patterns, e.g. if the staircase patternwas modified by adding a fourth rectangle adjacent to the middlerectangle, such a modified staircase has two paths which take intoaccount, among other dimensions, the widths of the two middle rectangleswhich could be different. In such a case, the method of FIG. 9Aidentifies the tightest range for an overall dimension of the rangepattern, i.e. the lowest maximum limit and the largest minimum limit.

In many embodiments, a method of the type illustrated in FIG. 9A isperformed twice, respectively for two adjacency matrices which in turnrespectively contain distances between edges oriented in horizontal andvertical directions. Note that the range data-structure of someembodiments has at least the following three integer fields: min, optand max. So a check is performed in the appropriately programmedcomputer to ensure legal values thereof, e.g. by testing if min <0 or=0or >0. Similar check is performed for legal values of max. Illegaloptimal values can arise as a result of incorrect user specification.Hence, the check for legal values is done twice in many embodiments:once to determine validity of user input and secondly to count andenumerate number of cutting slices. The user input is valid if and onlyif allowable range between adjacent line segments is greater than zero.Optimal values for edge (ij) can only be computed for an uninitializedrange if there is an alternate path between (ij) where all the edgeshave optimal values. In some embodiments, if the optimal value isillegal the matching process does not abort, as the optimal value is notvery critical.

In some embodiments of the invention, the number of sliced versions thatare required to represent a range pattern as described above inreference to acts 804A (vertical slicing) and 804B (horizontal slicing)are identified by programming a computer to perform a method of the typeillustrated in FIG. 10A. Typically, such a method checks if a range (fora dimension in the range pattern) spans across the zero value, e.g.whether the maximum limit is greater than or equal to zero, and/or theminimum limit is less than or equal to zero and accordingly identifiesthe number of sliced versions that are required. Specifically, in act1001, the computer copies an adjacency matrix into a temporary matrix“tempmat”.

Next, in act 1002, the computer performs a method of the type describedabove in reference to FIG. 9A, to compute any uninitialized dimensionsin the matrix. Thereafter, the computer goes to act 1003 and sets a flagcalled “multiple version” to FALSE. This flag indicates whether or notthe current range pattern can be represented by a single version thereofwhen sliced. Next, in acts 1004 and 1005, the computer initializes therespective variables I and J. Specifically, I is set to a value between0 and (number of rows of the adjacency matrix-2). Note that thisembodiment only evaluates an upper triangualar matrix, and so theformula for the upper limit on variable I's value is sufficient.Similarly, variable J is set to a value between I+1 and (number of rowsof the adjacency matrix-1).

Next, the computer checks, in act 1006, if the minimum limit fornode[I][J] is less than or equal to zero and the maximum limit fornode[I][J] is greater than or equal to zero, and moreover if the minimumlimit is not equal to the maximum limit. Whether or not the conditionsof act 1006 are met depend on the range pattern's geometric arrangementof edges therein and on the dimensions thereof, e.g. dimension Omax ofthe staircase range pattern (FIG. 2I) may have a minimum limit which isnegative for the range pattern to cover a pattern wherein the rectangle221 does not overlap rectangle 223 in the vertical direction, and amaximum limit which is positive for the range pattern to cover a patternwherein the rectangle 221 does overlap rectangle 223. In the staircaserange pattern (FIG. 2I), the dimension Omax may have both limitsnegative if the range pattern only covers patterns wherein rectangle 221always does not overlap rectangle 223. Similarly, the dimension Omax mayhave both limits positive if the range pattern only covers patternswherein rectangle 221 always overlaps rectangle 223.

If the conditions are met in act 1006, the computer proceeds to act1007, and alternatively if the conditions are not met the computerproceeds to act 1016 without changing the flag. In act 1007, thecomputer saves the minimum and maximum limits of node[I][J] andnode[J][I] in the local variables Ijmin, JImin, IJmax, JImax (i.e. makescopies thereof) and subsequently (as discussed next), the method callsitself recursively for each of two or three subranges that are presentwithin the current range. Specifically, the computer goes to act 1008and checks if the minimum limit for the node[I] [J] is less than zeroand the maximum limit for this node[I][J] is greater than zero, i.e. therange contains subranges for positive values, zero and negative values.As discussed above, in the staircase range pattern (FIG. 2I), thedimension Omax having a positive subrange covers rectangle 221overlapping rectangle 223, a negative subrange covers rectangle 221 notoverlapping rectangle 223, and the zero subrange covers rectangle 221touching rectangle 223 (in the vertical direction only—not physically).

If so, the computer goes to act 1013 and covers the positive range byrecursing the method of FIG. 10A after setting the minimum limit ofnode[I][J] to the value 1 and the maximum limit of node[I][J] to thevalue −1. On returning from recursing in act 1013, the computer goes toact 1014 to cover the zero range, by recursing the method of FIG. 10Aafter setting the minimum and maximum limits for node[I][J] andnode[J][I] to the value 0. On returning from recursing in act 1014, thecomputer goes to act 1015 to cover the negative range, by recursing themethod of FIG. 10A after setting the minimum limit of node[I][J] to thevalue IJmin, the maximum limit of node[J] [I] to the value JImax, themaximum limit of node[I][J] to -1 and the minimum limit of node[J][I]to 1. On completion of recursing in act 1015, the computer goes to act1012 to set the flag “multiple version” to TRUE, and thereafter goes toact 1016.

In act 1016, the computer checks if the flag “multiple version” is TRUE,or if iteration on variable J is completed and if not the computerreturns to act 1005 (described above). If the answer in act 1016 is yes,then the computer proceeds to act 1017 and checks if the “multipleversion” flag is TRUE or if the looping on variable I has been completedand if both conditions are not met the computer returns to act 1004(described above). If the answer in act 1017 is yes, the computerproceeds to act 1018 to check if the “multiple version” flag is FALSEand if so goes to act 1019 wherein the computer increments a counter forthe number of sliced versions, and thereafter returns. If the answer inact 1018 is no, the computer returns without incrementing the number ofsliced versions.

In act 1008, if the answer is no, the computer proceeds to act 1009 tocheck if the minimum limit is less than zero and the maximum limit isequal to 0 for the node[I][J]. If the answer is yes in act 1009, thenthe computer goes to act 1014 (described above). If the answer in act1009 is no, the computer proceeds to act 1050 to check if if the minimumlimit is equal to zero and the maximum limit is greater than 0 for thenode[I][J]. If the answer in act 1050 is yes, the computer proceeds toact 1010 to cover the positive range. Specifically, in act 1010, thecomputer sets the minimum limit of node[I][J] to 1 and the maximum limitof node[I][J] to −1 and thereafter recurses by performing the samemethod illustrated in FIG. 10A. After completion of recursion in act1010, the computer proceeds to act 1011 to cover the zero range.Specifically, in act 1011, the computer sets the minimum limit and themaximum limit for the node[I][J] and for the node[J][I] to the valuezero, and thereafter recursively performs the method shown in FIG. 10A.On completion of recursing in act 1011, the computer proceeds to act1012 (described above). Note that in act 1050 if the answer is no, thenthe computer proceeds to act 1016 (described above).

In some embodiments of the invention, acts 812A and 812B (describedabove in reference to FIG. 8D) are performed in a manner similar oridentical to that described above in reference to FIG. 10A, except thatact 1019 is replaced with another act 1020 as illustrated in FIG. 10B.Specifically, in act 1020, the computer generates each of one or moresliced versions of the range pattern, by traversing the range patternfrom one end to the other end (transverse to slicing direction), andidentifying each slice in the sliced version. In some embodiments, thecomputer checks if there is a change in an element of a row relative toits previous row, and starts a new slice if a change is found. Note thatin FIG. 10C acts 1021 or 1022 are implicitly defining slice boundaries.In other embodiments, the computer performs other acts to identifyboundaries between slices, e.g. by use of each pair of adjacent edges ina given direction (e.g. horizontal) to define a slice. For example, ifR1.t and R1.b are used as the pair of adjacent edges, the computer maybe further programmed to use R1.t-R1.b to define the slice's widthrange.

Exemplary acts which are performed by the computer in some embodimentsof the invention are illustrated in FIG. 10C, described next.Specifically, in some embodiments of the invention, the computer isprogrammed to sort all of the vertical edges horizontally and thehorizontal edges vertically, in the respective topological orders, inacts 1021 and 1022 respectively. Thereafter, in act 1023, the computerchecks if the direction of slicing of the sliced range pattern is in thehorizontal direction, and if so the computer goes to act 1026. In act1026, the computer scans the horizontal edges vertically, to determinethe boundary of each horizontal slice, and thereby to compute a rangefor the height of each horizontal slice.

Next, in act 1027 the computer scans vertical edges horizontally tocompute, for a given horizontal slice, the range of each fragment'swidth range (i.e. the minimum limit and the maximum limit). Thereafter,the computer loops on this act 1027 until each horizontal slice isprocessed, i.e. all fragments have been identified. Next, in act 1028,the computer of converts the distance is between two or morenon-adjacent edges of the range pattern into additional constraints.Thereafter, in act 1029, the computer stores in computer memory, theslices, fragments and constraints which have been generated for acurrent sliced version of a current range pattern.

In act 1023 if the answer is no, i.e. the slicing direction is vertical,and therefore the computer goes to act 1024, which is similar to act1026 (described above), except that vertical edges are now scannedhorizontally, to compute a range for the width of each vertical slice.Next, in act 1025, which is similar to act 1027, the computer scans thehorizontal edges vertically to compute a range for each fragment'sheight. Act 1025 is performed repeatedly for each vertical slice thatwas identified in act 1024, and on completion thereof the computer goesto act 1028 (described above).

In some embodiments of the invention, the computer is programmed to usesliced versions of the range patterns (which are held in a library inthe computer memory) to identify one or more locations in a layout thatare likely to be poorly printed, i.e. result in hot spots duringfabrication, as illustrated in FIG. 11A. Specifically, in suchembodiments, the computer performs an act 1101 in which a coarse grid isused to identify any blocks of an IC layout that match a range patternin the library. Act 1101 uses a coarse grid to quickly screen out largeportions of the IC layout that are unlikely to match a range pattern.Thereafter, in act 1102, the computer uses a fine grid to identifyshapes in the IC layout that match range patterns in the library, fromamong layout blocks that matched a range pattern at the coarse level inact 1101.

Next, in act 1103, the computer automatically eliminates one or morematches (also called “occurrences”) of the range patterns that areredundant with one another, i.e. duplicates, e.g. by checking if theirlayout locations are within a predetermined distance from one another.The predetermined distance may be less than, for example, minimumfeature size in the IC layout (or a fraction thereof) in someembodiments, while in other embodiments the predetermined distance maybe specified based on a manufacturing grid or a minimum resolution ofthe process to be used in fabricating the IC layout. After act 1103, thecomputer goes to act 1104 and checks if all the range patterns have beenchecked in all directions, and if so the computer returns with thematches that have been found so far.

In redundancy checking of some embodiments, only matches withoverlapping boundaries in both horizontal and vertical directions arechecked. Otherwise, they are all regarded as different matches in suchembodiments. A simple method for checking redundant matches compareseach pair of matches to one another, to see if they refer to the sameoccurrence, although it is time-consuming. Some embodiments adopt a morecomputationally efficient solution by sorting the bottom left corner ofthe matches first in horizontal direction and then sorting matches,whose bottom left corners are standing on the same vertical line, in thevertical direction. In that way, these embodiments only compare adjacentmatches in a sorted queue.

In act 1104, if all four orientations of each range pattern (orientedEast, West, North, South) relative to the IC layout have not beenchecked for matches, and then the computer goes to act 1105, wherein therange patterns are rotated by 180 degrees (assuming a specific directionfor the range patterns was not specified) and thereafter the computerreturns to act 1101. One or more directions for each range pattern maybe specified, for example, by a fabrication facility (“fab”), or by theuser when defining the range pattern, in which case occurrences ofpatterns in the IC layout are checked for coverage by the range patternonly the specified direction(s).

In some embodiments of the invention, a computer is programmed toperform the method of FIG. 11B, to identify one or more locations in alayout that match a range pattern in a library of the computer's memory.Specifically, in act 1111, the computer sets the grid size for a coarsestage (to be performed by the method in FIG. 11B), e.g. the value 50 nmis typically used. The grid size may be selected to be sufficientlysmall so that each rectangle in the layout is larger in its smallestdimension than the selected grid size. If the minimum width of a tracein the layout is 90 nm, then the grid size for the coarse grid may beselected to be less than 45 nm. The specific value chosen for the gridsize typically involves a tradeoff between the amount of CPU time andresources required to perform the method of FIG. 11B (which increases asthe grid size is reduced) and the number of false positives that arelikely to be identified (which increases with larger grid size). Notethat an increase in the number of false positives increases the amountof work to be done by another stage that uses a fine grid (describedbelow) to screen out the false positives, e.g. as illustrated in FIG.11C.

Next, in act 1112, the computer digitizes the sliced version of a rangepattern, specifically by mapping the sliced version to the coarse grid,for example as described below in reference to FIG. 12A. Note that thedigitization can be performed in any manner as will be apparent to theskilled artisan, in view of one specific embodiment illustrated in FIG.12A. Next, in act 1113, the computer encodes the sliced version, e.g. byconverting bits in a sequence that represent the presence and absence ofmaterial in a slice into an encoded value for the slice. Encoding ofslices can be performed as illustrated in one embodiment in FIG. 12B.

Thereafter, in act 1114, the computer sets N1 and N2 to be the number ofrows and columns respectively of the matrix resulting from mapping ofthe IC layout onto a coarse grid. In a typical IC layout, note that N1and N2 will be in the range of a million. Next, in act 1115, thecomputer sets m1 and m2 to be the maximum number of rows and columnsrespectively of the matrix resulting from mapping of the sliced versionof the range pattern to the coarse grid. Note that the values for m1 andm2 are typically in the range of 1 μm, which translates into 15 to 20grid units depending on the grid size. Thereafter, in act 1116, thecomputer sets the row index zero. Next, the computer goes to act 1117and checks if the sum (rowIndex+m1+1) is less than N1, and if so thecomputer performs acts 1118-1127, which are described next. Note thatthe overlap is “m1+1” and not just m1 to round up (instead of rounddown) the overlap distance when expressed in grid units.

Specifically, in act 1118, the computer sets the column index to zero,and then proceeds to act 1119. In act 1119, the computer checks if(colIndex+m2+1) is less than N2, and if so the computer performs thefollowing acts 1120-1125. Specifically, in act 1120, the computerinitializes a bottom left corner of a moving window (e.g. window 616illustrated in FIG. 6D). In one embodiment, the computer holds in memorya data structure for the moving window which includes the followingfields: b1X, b1Y, colNum, and rowNum. The fields b1X, b1Y indicatethe×coordinate and the y coordinate respectively of the bottom leftcorner of the moving window, while the fields colNum, and rowNumindicate the height and width of the moving window respectively. Thefields colNum, and rowNum are typically both set to 1000, although asmaller or larger window may be used in other embodiments. Note that toavoid missing patterns in the layout that are covered by a rangepattern, the moving window's dimensions should be at least as large asthe largest dimensions in the range pattern.

In one embodiment, the field b1X is set to collndex, and the field b1Yis set to rowlndex in an act 1120. Next, in act 1121, the computer mapsthe original layout matrix to the coarse grid, and obtains therefrom, asubmatrix of size equal to the moving window. In some embodiments, theentire layout is not first mapped onto the coarse grid as indicated byact 1121 in FIGS. 11B and 18. Instead, in these embodiments, the layoutis mapped to the coarse grid incrementally, for example in someembodiments only the layout contained in the moving window is mapped tothe coarse grid.

While the submatrix may be obtained from any location in the originallayout matrix, in some embodiments the location is selected to be thebottom left corner of the layout matrix, and the location is changed bymovement of the window in the manner described above in reference toFIGS. 6D and 6E. Next, in act 1122, the computer compares a slicedversion of the range pattern to the submatrix of the layout, and in act1123 records any matches that have been identified during suchcomparison. Typically, the computer records in its computer memory theboundaries of each region covered by location of a moving window 616(FIG. 6D) in which a match was found (“coarsely matched region”) andalso an identity of the sliced version of the range pattern whichmatched the layout within moving window 616. The comparison in act 1121is performed in any manner, as described above in reference to act 805in FIG. 8A. Such comparison may involve, for example, moving a blockwithin the moving window in the manner illustrated in FIG. 6G (describedabove).

Next, in act 1124, the computer increments collndex by colNum−(m2+1), soas to maintain an overlap between two adjacent moving windows, of atleast m2+1 as described above in reference to FIG. 6D. As noted above,colNum and rowNum are both typically of value 1000 for a square shapedmoving window of size 1000. Next, in act 1125, the computer checks ifthe looping on colindex has been completed and if not returns to act1119. If the looping has been completed on colIndex in act 1125, thecomputer proceeds to act 1126. In act 1126, the computer incrementsrowlndex by rowNum—(m1+1). Thereafter, the computer goes to act 1127 andchecks if looping on rowindex has been completed and if completed thenthe computer returns from performing the method in FIG. 11B, andotherwise if not completed the computer returns to act 1117 (describedabove).

Matches that have been recorded in act 1121 are verified in someembodiments, using a finer grid size than the grid size used in themethod of FIG. 11B. Specifically, the “coarse matched region” in which amatch was recorded in act 1123 (FIG. 11B) is enlarged in someembodiments to another window 1129 (FIG. 11C). Window 1129, alsoreferred to as a matching window is obtained by expanding the“coarse-matched region” by a predetermined amount in all directions,e.g. by one row or one column (i.e. one grid unit) on each of four sidesbut centered at the same center as window 616. Although in this example,the matching window 1129 is obtained by expanding the boundaries of acoarse matched region by just one grid unit, in other examples othernumber of grid units may be used, for example 8 grid units are used insome embodiments to obtain a matching window from the coarse matchedregion.

Expansion of the window as illustrated in FIG. 11C enables the computer,for example, to check that boundary values around a pattern in thelayout are in fact zero (confirming that the layout's pattern matchesthe range pattern even at the boundaries, and such a check is alsocalled “strict check”). Such a matching window 1129 is used in someembodiments, by a method of the type illustrated in FIG. 11C, to verifyby use of a fine grid size the presence of a pattern in the IC layoutwhich matches the range pattern identified in act of 1123. Specifically,in act 1131, the computer sets the grid size to a fine grid size, whichis typically selected based on the size of a manufacturing grid. In someembodiments the fine grid has the same grid size as the manufacturinggrid, e.g. 5 nm.

Next, a sliced version of range pattern that is identified in act 1123is mapped to the fine grain, i.e. digitized. Thereafter, in act 1133,the computer encodes the digitized sliced version of the range pattern(based on a sequence of bits representing the presence and absence ofmaterial, as described elsewhere herein), and then goes to act 1134. Asnoted above, each slice of a sliced version of the range patternincludes a number of fragments, and each fragment is a matrix of 0s or amatrix of Is. During encoding in act 1113, the computer of someembodiments replaces each matrix of 0s by a single 0 and also replaceseach matrix of I s by a single 1. The computer of these embodimentsfurther replaces each slice by a string of alternating 0s and 1s. Thenumber of bits (i.e. 0s and 1s) in each slice's encoded value depends onthe number of fragments therein. As noted above, in some embodiments, anadditional bit 1 is encoded as the most significant bit of such anencoded value.

Next, in act 1134 (or in a subsequent act 1141) the computer checks forconditions to loop over acts 1135-1140, for example checks if thelooping has been performed for each occurrence of the sliced version ofthe range pattern saved to computer memory in act 1123. As will beapparent to the skilled artisan, in most programming languages, eitherone of the two acts 1134 and 1141 are required, but not both. Afterentering the loop, in act 1135, the computer determines from computermemory the×coordinate and the y coordinate of the matching window whichwas saved in act 1123 as identifying the occurrence of the pattern inthe layout. Next, in act 1136, the computer maps a sublayout within thematching window on to the fine grid.

Thereafter, in act 1137, the computer searches this sublayout using theencoded values of slices in the sliced version (which were encoded inact 1133). If during this searching in act 1137, a match is found, thenin some embodiments the computer is programmed to further calculate ascore for the matching occurrence in act 1138, using optimal value(s)and scoring function(s) which are also stored in the computer memory asdescribed above in reference to FIG. 2J. In some embodiments, the closerthe dimensions of the matching pattern in the layout to optimal valuesof the range pattern, the higher the score, although an inverse of sucha scoring function may be used in other embodiments.

In act 1139, the computer determines a match location in actual layout.Next, in act 1141, the computer checks if each match saved in act 1123has been verified using the fine grid as just described, and if so thismethod of FIG. 11C is completed and the computer returns. If in act1141, the answer is no, the computer proceeds to act 1134 (describedabove).

In some embodiments of the invention, acts 1132 and 1112 described aboveare implemented, to convert the dimensions in a sliced version of therange pattern into grid units (i.e. wherein grid size constitutes a gridunit), as illustrated in FIG. 12A. Specifically, in act 1201, thecomputer makes a copy of a sliced version of the range pattern, andthereafter goes to act 1202. In act 1202, the computer initializes avariable N to be equal to the number of slices in the sliced version.Next, in act 1203, the computer initializes two variables minCN andmaxCN to the value 0. These two variables respectively represent theminimum limit and the maximum limit on the width of the range pattern,expressed in number of columns. Then the computer goes to act 1204wherein a loop variable I is set (initially to zero and incremented toN-1) for looping over acts 1205-1221. Then, in act 1205, the computersets slice [I]'s minimum limit for its width to be equal to (minimumlimit/grid size). Note that the grid size can be different depending onwhether a coarse grid or a fine grid is in use when this method isinvoked.

Next in act 1206 the computer checks if there is an optimum value in thecurrent slice's width, and if so sets slice [I]'s optimum value forwidth=(optimum value/grid size). Then in act 1207, the computer setsslice [I]'s maximum limit for width=R0UNDUP (maximum limit/grid size).Note that the function R0UNDUP performs a rounding up of a number'sfraction value to the next whole number. Thereafter in acts 1208 and1209, the computer increments minCN by the slice [I]'s minimum limit forwidth, and similarly increments maxCN by slice [I]'s maximum limit forwidth. Next, in act 1210, the computer initializes another variable M tobe number of fragments in slice [I]. Then in act 1211, the computerinitializes two variables minRN and maxRN to zero. These two variablesrespectively represent the minimum limit and the maximum limit on thelength of slice [I], expressed in number of rows.

Then, the computer proceeds to act 1212 to set up the looping variable J(initially to zero and incremented to M-1) for looping over acts1213-1220. Acts 1213-1217 convert the dimensions of fragments in amanner similar to the above-described acts 1205-1209. Specifically, inact 1213, the computer sets fragment [J]'s minimum limit for its lengthto be equal to (minimum limit/grid size). Next in act 1214 the computerchecks if there is an optimum value in the current fragment's length,and if so sets fragment [J]'s optimum value for length=(optimumvalue/grid size). Then in act 1207, the computer sets fragment [J]'smaximum limit for length=R0UNDUP (maximum limit/grid size). Next, inacts 1216 and 1217, the computer increments the respective variablesminRN and maxRN in the above-described manner, but now using thecorresponding values of the fragment's limits.

Next, in acts 1218 and 1219, the computer sets two variables totalMinRNand totalMaxRN to corresponding values minRN and maxRN if thesecorresponding values are greater. Note that variables totalMinRN andtotalMaxRN are initialized (not shown in FIG. 12A) to the respectivevalues minRN and maxRN for the very first slice, i.e. when I is zero.Variables totalMinRN and totalMaxRN represent the overall limits for therange pattern as a whole, across all slices. Then the computer proceedsto act 1220 to check if it's done with looping on each fragment and ifnot, returns to act 1212 and if done then it goes to act 1221. In act1221, the computer checks if it is done with looping on each slice, andif not returns to act 1204, and if done then this method (of FIG. 12A)is completed and the computer returns, to an appropriate one of acts1132 and 1112 from which this method was invoked.

In some embodiments of the invention, encoding of a sliced version ofthe range pattern as described above in reference to FIGS. 11B and 11C,in the respective acts and 1113 and 1133 is performed as described nextin reference to FIG. 12B. Specifically, in act 1231, the computer sets Nto be the number of slices in the sliced version, and thereafter goes toact 1232. In act 1232, the computer sets a loop variable J to a value inthe range 0 to N-1. Next, in act 1233, the computer sets the encodedvalue of slice [J] to be the value 1 which will form the prepended bit“1” in the final encoded value on completion of this method.Specifically, as noted above in reference to FIG. 5E, a bit “1” isprepended to be the most significant bit in some embodiments, in orderto distinguish between bit sequences with a leading 0 and sequences witha leading 1 (obtained from digitized data).

Next, in act 1234, the computer sets M to be the number of fragments inslice [J]. Then the computer goes to act 1235 and sets the loopingvariable I to have a value in the range 0 and M-1. In severalembodiments, the computer actually counts down, i.e. starts with M-1 asan initial value for the looping variable I, followed by decrementingthis value in the next iteration. Next, in act 1236, the computer shiftsthe previously encoded value to the left by one bit, and then adds thecurrent value. Specifically, the computer sets the encoded value ofslice [J] to be equal to (previously encoded value times two)+thecurrent value of fragment [I] in slice [J]. Note that the resultingvalue will be thereafter shifted to the left once again in the nextiteration and the next fragment's value is added herein.

Hence, an encoded value for a current slice is assembled, one fragmentat a time. Note that acts 1235 and 1236 together replace each matrix (of0s or 1s) for a fragment, by a single value (of 0 or 1) for thatfragment, to implement a modified form of run length compression. Thejust-described encoding differs from traditional run length compressionbecause the length of each bit (0 or 1) is not present within thisencoded value. Instead, in such embodiments, the length of each fragmentis maintained separately, in a field in the computer memory accessed bya data structure for the range pattern as illustrated in FIG. 8B.

Use of such an encoded value speeds up comparison of a slice in thelayout to a slice in the range pattern, although a false positive can beidentified by such comparison because specific dimensions are notcompared when just the encoded values are compared. After act 1236, thecomputer goes to act 1237 and checks if looping on each of the fragmentsof the current slice has been completed and if not returns to act 1235.If looping has been completed in act 1237, the computer goes to act1238. In act 1238 the computer checks if the looping has been completedon each slice in the sliced version, and if so returns to whichever stepinvoked this method and if the looping has not been completed then thecomputer returns to act 1232.

In some embodiments of the invention, comparison acts 1122 (FIG. 11B)and 1137 (FIG. 11C) are performed by implementing acts 1301-1310 asillustrated in FIG. 13A. Note that “VerifyOccurrence” is called in“WindowRPM” regardless of whether “WindowRPM” is invoked by“CoarseGridFilter” OR “FineGridVerifier”. Specifically“VerifyOccurrence” is required at each stage to perform the checks onslice widths and fragment lengths and checks on other additionalconstraints.

Specifically, in act 1301, the computer sets N to be the number ofcolumns in the layout matrix. Next, in act 1302, the computer computesminR and maxR as the minimum and maximum possible number of rows of allsliced versions of the range pattern which is been currently selected.Next, in act 1303, the computer initializes looping variables for acts1304-1313. Specifically, the computer loops over all possible blocks Bof columns size N and a row number between minR and maxR within thelayout. While in some embodiments of act 1303, the computer isprogrammed to perform worm-like movement of a block as illustrated inFIG. 6G (described above), in other embodiments the computer isprogrammed to simply enumerate the blocks. The simple enumeration isperformed, by starting with a block whose length is equal to the lengthof the matching window and whose height is equal to minR followed byincreasing the height to maxR in an incremental manner, one row at atime, and when the block is of size maxR, the computer shifts the wholeblock up by one row (which represents one unit of grid size).

Next, the computer goes to act 1304 and initializes another loopingvariable I for looping over each slice in the current block B.Thereafter, the computer performs act 1305 to compute the width forslice [I] (e.g. by detecting a change in adjacent columns) and storesthis value. Specifically, in some embodiments, the computer uses a blockin the layout whose length is equal to the length of the matchingwindow, and whose height is equal to minR and thereafter slices thislayout block in the vertical direction by moving from left to right andchecking if each successive column is same as the previous column and ifnot a slice is deemed to be completed (i.e. a slice boundary isdetected), and a new slice is begun. In this manner, the boundary of acurrent slice [I] is identified and stored into computer memory. In act1305, the computer also computes the length of each fragment within aslice. Next, the computer goes to act 1306 and compresses slice [I]using a modified run length compression as discussed above in referenceto acts 1235 and 1236 in FIG. 12B. Next, in act 1307, the computerencodes the sequence of bits for slice [I] into an integer as describedabove, i.e. after prepending the bit “1” as its most significant bit,and stores the integer as the slice's encoded value. Thereafter, thecomputer goes to act 1308 and checks if looping on each slice has beencompleted and if not returns to act 1304.

In act 1308, if the looping has been completed on all of the slices, asidentified by traversing the length of the block of the computerproceeds to act 1309. In act 1309, the computer computes a onedimensional string of integers (encoded values) of all of the slices inthe current block. Thereafter, the computer goes to act 1310 and invokesa string matching method for comparing the one dimensional string fromact 1309 to a corresponding string for encoded values of slices in therange pattern.

While any string matching method may be used, one illustrativeembodiment uses a specific method called “Knuth-Morris-Pratt algorithm”shown in FIG. 13B (abbreviated as KMP method). The method of FIG. 13Buses a prefix function PFX[q], which is the length of the longest prefixof the string P that is also a proper suffix of the string Pq.Computation of the prefix function is shown in FIG. 13C. Note that theKMP algorithm (as used in text string matching) is well known in theart, and hence it is not described any further herein.

Next, in act 1311, the computer checks, for each occurrence of apotential match from act 1310, as to whether or not the potential matchis confirmed by use of the current grid (coarse grid or fine griddepending on the current stage of processing). Next, the computer goesto act 1312 and records the occurrence of a verified match, ifverification is successful in act 1311 and if verification is notsuccessful the match is screened out. Next, the computer goes to act1313 and checks if looping is completed on each block in the window andif not returns to act 1303, to perform the same acts for a new block. Iflooping has been completed on all blocks, i.e. the window has beencompletely traversed by block enumeration, then the computer returnsfrom the method in FIG. 13A to whichever act invoked this method.

Act 1311 of FIG. 13A is performed in some embodiments by the methodillustrated in FIG. 13D. Specifically, in act 1331, the computer sets Nto be the number of slices in the sliced version of the range pattern,and thereafter goes to act 1332 to set the value of a loop variable I tobe in the range 0 to N-1. Thereafter the computer goes to act 1333 toreport a false match if the slice in the range pattern has a minimumlimit greater than the length of the slice in the block of the layout,or if the maximum limit of the slice of the range pattern is less thanthe block's slice length.

Thereafter, the computer repeats the above-described act 1333, to checkon the dimensions of fragments in each slice [I]. Specifically, in act1334, the computer sets M to be the number of fragments in current slice[I]. Thereafter the computer goes to act 1335 and sets the loop variableJ to be a value in the range 0 to M-1. Then the computer goes to act1336 to report a false match if the fragment [J] in the slice [I] has aminimum limit greater than the length of the fragment in the slice inthe block of the layout, or if the maximum limit of the fragment in therange pattern is less than the block's fragment's length.

Next, the computer goes to act 1337 to check if looping has beencompleted on each fragment of a current slice [I] and if not thecomputer returns to act 1335. If looping has been completed in act 1337,the computer goes to act 1338 to check if looping has been completed oneach slice of the range pattern, and if not the computer returns to act1332. If looping has been completed on each slice, the computer goes toact 1339, to determine whether all constraints of the range pattern aresatisfied. Specifically, in act 1339, the computer initializes anylooping parameter (e.g. specified in the range pattern's data structureas the total number of constraints therein), and thereafter goes to act1340 to check if a constraint that is specified in the range pattern issatisfied. If so, the computer goes to act 1342 to determine whether allconstraints have been checked. If not checked, the computer returns toact 1339. When act 1342 determines that all constraints have beenchecked, the computer goes to act 1343 and reports a true match, andthereafter returns from performance of the current method (shown in FIG.13D). In act 1340, if the constraint is not satisfied, the computer goesto act 1341 to report a false match, followed by returning from thecurrent method.

Any lithography hotspot detection method of the type described above maybe used in a digital AS1C design flow, which is illustrated in FIG. 14Bin a simplified exemplary representation. At a high level, the processof designing a chip starts with the product idea (1400) and is realizedin a EDA software design process (1410). When the design is finalized,it can be taped-out (event 1440). After tape out, the fabricationprocess (1450) and packaging and assembly processes (1460) occurresulting, ultimately, in finished chips (result 14140).

The EDA software design process (1410) is actually composed of a numberof stages 1412-1430, shown in linear fashion for simplicity. In anactual AS1C design process, the particular design might have to go backthrough steps until certain tests are passed. Similarly, in any actualdesign process, these steps may occur in different orders andcombinations. This description is therefore provided by way of contextand general explanation rather than as a specific, or recommended,design flow for a particular AS1C. A brief description of the componentsof the EDA software design process (stage 1410) will now be provided.

System design (stage 1412): The circuit designers describe thefunctionality that they want to implement, they can perform what-ifplanning to refine functionality, check costs, etc. Hardware-softwarearchitecture partitioning can occur at this stage. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stageinclude Model Architect, Saber, System Studio, and DesignWare® products.

Logic design and functional verification (stage 1414): At this stage,the VHDL or Verilog code for modules in the system is written and thedesign (which may be of mixed clock domains) is checked for functionalaccuracy. More specifically, the design is checked to ensure that itproduces the correct outputs. Exemplary EDA software products fromSynopsys, Inc. that can be used at this stage include VCS, VERA,DesignWare®, Magellan, Formality, ESP and LEDA products.

Synthesis and design for test (stage 1416): Here, the VHDL/Verilog istranslated to a netlist. The netlist can be optimized for the targettechnology. Additionally, the design and implementation of tests topermit checking of the finished chip occurs. Exemplary EDA softwareproducts from Synopsys, Inc. that can be used at this stage includeDesign Compiler®, Physical Compiler, Test Compiler, Power Compiler, FPGACompiler, Tetramax, and DesignWare® products.

Design planning (stage 1418): Here, an overall floorplan for the chip isconstructed and analyzed for timing and top-level routing. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stageinclude Jupiter and Flooplan Compiler products.

Netlist verification (stage 1420): At this step, the netlist is checkedfor compliance with timing constraints and for correspondence with theVHDL/Verilog source code. Exemplary EDA software products from Synopsys,Inc. that can be used at this stage include VCS, VERA, Formality andPrimeTime products.

Physical implementation (stage 1422): The placement (positioning ofcircuit elements) and routing (connection of the same) occurs at thisstep. Exemplary EDA software products from Synopsys, Inc. that can beused at this stage include the Astro product. Note that the output ofthis stage 1422 may be used in lithography hotspot detector 1439 asshown in FIG. 14B. Various embodiments of a lithography hotspot detector1439 have been illustrated and described above in reference to FIGS. 2Aet seq. After reviewing the results displayed by lithography hotspotdetector 1439, if not satisfied, a chip designer (FIG. 14A) may go backto stage 1422 to rip up and re-route portions of the layout as describedabove.

Although circuitry and portions thereof (such as rectangles) may bethought of at this stage as if they exist in the real world, it is to beunderstood that at this stage only a layout exists in a computer 150(FIG. 14A) which has been programmed to implement a lithography hotspotdetector 1439. The actual circuitry in the real world is created afterthis stage as discussed below.

Analysis and extraction (stage 1424): At this step, the circuit functionis verified at a transistor level, this in turn permits what-ifrefinement. Exemplary EDA software products from Synopsys, Inc. that canbe used at this include Star RC/XT, Raphael, and Aurora products.

Physical verification (stage 1426): At this stage various checkingfunctions are performed to ensure correctness for: manufacturing,electrical issues, lithographic issues, and circuitry. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this includethe Hercules product.

Resolution enhancement (stage 1428): This involves geometricmanipulations of the layout to improve manufacturability of the design.Exemplary EDA software products from Synopsys, Inc. that can be used atthis include iN-Phase, Proteus, and AFGen products.

Mask data preparation (stage 1430): This provides the “tape-out” datafor production of masks for lithographic use to produce finished chips.Exemplary EDA software products from Synopsys, Inc. that can be used atthis include the CATS(R) family of products. Note that lithographyhotspot detector 1439 may also be used with the output of this stage1430, in some embodiments in accordance with the invention. Actualcircuitry in the real world is created after this stage, in a waferfabrication facility (also called “fab”).

The data structures and/or software code for implementing one or moreacts described in this detailed description can be encoded into acomputer-readable medium, which may be any article of manufacture, suchas a storage medium and/or a transmission medium that can hold codeand/or data for use by a computer. Hence one article of manufacture inaccordance with the invention can be any storage medium includes, but isnot limited to, magnetic and optical storage devices such as disk drivescontaining one or more hard disk(s) or floppy disk(s), tape drivescontaining one or more magnetic tape(s), optical drives containing oneor more CDs (compact discs) and/or DVDs (digital versatile discs).Moreover, another article of manufacture in accordance with theinvention can be any transmission medium (with or without a carrier waveupon which the signals are modulated) which includes but is not limitedto a wired or wireless communications network, such as the Internet.

In one embodiment, the article of manufacture includes computerinstruction signals for carrying out one or more acts performed bymethods illustrated in FIGS. 3A et seq, and the computer instructionsignals are present in a storage medium and/or a transmission medium. Inanother embodiment, such an article of manufacture includes computerdata signals representing a range pattern, as illustrated in FIGS. 2A etseq, with or without computer instruction signals that use the rangepattern.

Note that a computer system 150 used in some embodiments to implement ahotspot detector 1439 of the type described herein uses one or morelinux operating system workstations (based on IBM-compatible PCs) and/orunix operating systems workstations (e.g. SUN Ultrasparc, HP PA-RISC, orequivalent), each containing a 2 GHz CPU and 1 GB memory, that areinterconnected via a local area network (Ethernet).

FIGS. 15A and 15B illustrates data provided in a pattern format file insome embodiments of the invention, to specify a pattern in the cuttingslice representation. Specifically, in FIG. 15A, the following fourtypes of range constraints are specified. W for width. V for fragmentheight. U represents a unique value for a dimension (e.g. width orheight) in the layout, which can be greater than or equal to specifiedvalue. The value U is only to be used for boundary values, and it meansthe value of the dimension is no less than the specified value. Fornon-boundary values of a dimension, instead of value U, the range flag Ris to be used, as described below. Note that U values smaller than thecoarse grid size are typically eliminated to avoid loss of matches.Whenever a dimension's boundary value is no more than the coarse gridsize, the value is set as U to avoid missing matches.

In FIGS. 15A and 15B, R stands for range (slice width or fragment heightin layout should be within specified range, and if the range is on theboundary, the computer must check outside the boundary of the matchedarea to make sure the dimension is really within the range). O and Rstand for optimal value with a range (similar to just range R but withthe addition of an optimal value O, which is used to calculate thematching score). D for don't care (any non-zero value for thedimension). The D symbol specifies a value for a dimension that is notconstrained. However in one implementation, the computer simply countsthe dimension's D value as 1. Therefore, a good practice is to avoidusing D values too much so that the range of the number of rows orcolumns cannot be computed as the real pattern specification. Sometimesthe user may use R to specify a range though there is no rangeconstraint on the original pattern. Enforcing a redundant rangeconstraint on a value does not cause the loss of any matches.

In these FIGS. 15A-15B, the following symbols are specified. Crepresents the length of repetition of the value in the verticaldirection (e.g. C 2,1 1 refers to repetition length of C_(2,1)). S isthe width of the slice (e.g. S 3 refers to width of slice S₃). The lastvalue in V C 2,1 1 is the coefficient of the item. The combination ofall such items forms a polynomial expression. After the value section ofthe polynomial, there is a section for the right hand values, with fourtypes of values as follows. R represents range formed by the two righthand values. G represents greater than or equal to. L represents lessthan or equal to. E represents equal to. Equations are typicallyconstructed using the right hand values, to specify constraints betweenslices.

Numerous modifications and adaptations of the embodiments describedherein will become apparent to the skilled artisan in view of thisdisclosure. For example, the data structure illustrated in FIG. 2D canbe used to represent patterns composed of any shapes (such as shapesused for optical proximity correction), although many embodiments arelimited to patterns of only rectangles as illustrated in FIGS. 2A(“drill” pattern), 21 (“staircase” pattern), 5B (“door” pattern) and 5G(“mountain” pattern).

Although left boundary and bottom boundary of a range pattern are usedin some embodiments as known locations (as described above in referenceto FIGS. 2H and 2I), other embodiments may use other boundaries such asa left boundary and a top boundary in which case one or more left edgesof rectangle(s) located at the left boundary and one or more top edgesof rectangle(s) located at the top boundary are identified in therespective storage locations 214A and 214B as illustrated in FIG. 2J.

Moreover, although in some embodiments, for certain sequence of acts areperformed as illustrated in the attached figures and described herein,other embodiments perform such acts in a different order relative to theorder of that has been shown. For example, in FIG. 10C act 1022 isperformed after act 1021 in some embodiments, although in otherembodiments act 1022 is performed before act 1021. Furthermore, in eachof acts 1021 and 1022, sorting can be performed either on the maximumlimits or on the minimum limits depending on the embodiment.

Note also that methods of the type described herein are highlyparallelizable, in the sense that matching of each range pattern in alibrary can be performed independently by a corresponding number ofprocesses (and/or processors) each of which has a copy of the IC layout.

As another example, although in some embodiments the KMP algorithm isused, other embodiments use other string matching algorithms. Examplesof other string matching algorithms are well known in the art, and aredescribed in, for example: (1) a book entitled “EXACT STRING MATCHINGALGORITHMS” by Christian Charras and Thierry Lecroq, Laboratoired'Informatique de Rouen, Université de Rouen, Faculté des Sciences etdes Techniques, 76821 Mont-Saint-Aignan Cedex, FRANCE, available on theInternet at the address “www-igm.univ-mlv.fi%lecroq%string” (wherein theURL is obtained by replacing % with “m” and by preceding the addresswith http://), (2) an article entitled “A fast string matchingalgorithm” by RS Boyer and JS Moore, published in Communications of ACM,vol. 20, pp. 262-272, 1977 at“www.cs.utexas.edu%users%moore%publications%fstrpos.pdf”and (3) anarticle entitled “A Simple Fast Hybrid Pattern-Matching Algorithm” byFrantisek Franek, Christopher G. Jennings and W. F. Smyth, AlgorithmsResearch Group, Department of Computing & Software, McMaster University,Hamilton ON L8S 4K1, Canada, by Editors A. Apostolico, M. Crochemore,and K. Park in Sixteenth Annual Symposium on Combinatorial PatternMatching (CPM 2005), Lecture Notes in Computer Science, Vol. 3537, pp.288-297, 2005 Springer-Verlag Berlin Heidelberg 2005 available over theInternet at the address“www.cas.mcmaster.ca%˜franek%proceedings%cpm05.pdf.” The just-describedthree documents are incorporated by reference herein in their entirety,to illustrate alternative embodiments that use string matchingalgorithms different from the KMP algorithm.

For example, several embodiments of the invention are used after opticalproximity correction (OPC) in the resolution enhancement stage 1428 (seeFIG. 14B), and work as described above in reference to FIG. 5H. Notethat such embodiments do not use two grids as illustrated by acts 1101and 1102 in FIG. 11A and instead all matching is done on a single grid,which uses as its pitch the same distance as (or smaller distance than)a size of the manufacturing grid. Hence, if the manufacturing grid sizeis 5 nm for a given IC fabrication process, a single-grid embodiment mayperform act 332 of the type illustrated in FIG. 3C in a post-OPCactivity, using a grid of pitch 1 nm.

A single-grid method of some embodiments performs many of the same actsor similar acts as described above for two grid methods, except for thefollowing differences. The single-grid method performs acts 1603, 604and 1607 as illustrated in FIG. 16. FIG. 16 is derived from FIG. 6A byremoving therefrom the acts that are not performed in the single-gridmethod. Act 1603 in FIG. 16 is similar to act 603 except that the layoutmatrix is generated using the single grid. Moreover act 1607 is similarto act 607 except that matches are output in act 1607.

Similarly, FIG. 17 for a single grid method is derived from FIG. 11A,and act 1702 in FIG. 17 is similar to act 1102 in FIG. 11A, as it isapplied to a single grid. Moreover, FIG. 18 for a single grid method isderived from FIG. 11B, and acts 1811, 1814, 1815 and 1821 in FIG. 18 aresimilar to corresponding acts 1111, 1114, 1115 and 1121 in FIG. 11B asapplied to a single grid. Furthermore in FIG. 18, as shown in the dottedbox, acts 1838-1840 are performed between acts 1122 and 1124, and theseacts 1838-1840 are similar to corresponding acts 1138-1140 in FIG. 11Das applied to a single grid. Finally, FIG. 19 for a single grid methodis derived from FIG. 13A, and act 1911 in FIG. 19 is similar to act 1311in FIG. 13A, as it is applied to a single grid. Numerous suchmodifications to apply the various acts described herein to a singlegrid method will be apparent to the skilled artisan in view of thisdisclosure.

In several embodiments that use a single-grid method, the region of alayout within each window is supplied to one of several processors sothat one or more acts of the type described herein are performed inparallel (to one another). As another example, parallel processing isnot used in some embodiments wherein all regions of a layout are checkedby a single processor because speed is not a constraint, e.g. when theactivity is in the mask data preparation stage 1430 (FIG. 14B). As stillanother example, parallel processing is not used for layouts that fitwithin a single window, e.g. layouts for standard cells of a library fora given technology.

As will be apparent to the skilled artisan, the just-described standardcell library normally contains a number of cells which have both alogical and a physical representation. The logical representationdescribes behavior of the cell and can be represented by a truth-tableor boolean algebra equation. The physical representation is theimplementation of the logical description first as a netlist, which atits lowest level is a nodal description of transistor connections(commonly SPICE). After a transistor level netlist is created, adesigner's chip design can “layed-out” by synthesis, place and routeelectronic design automation (EDA) tools to create actual physicalrepresentations of the transistors and connections in a format that canbe manufactured (GDSII). The standard cell library is normally suppliedto a chip designer, by a fabrication facility such as TSMC (TaiwanSemiconductor Manufacturing Company Ltd.).

As another example, instead of scoring defective locations as describedabove in reference to the formula f for the scoring function, analternative embodiment performs range relaxation as follows.Specifically, this alternative embodiment starts by initially checking alayout by using a set of range patterns that have a large score (i.e.highest yield impact), which identifies defective locations of highestpriority. The alternative embodiment follows this initial checking, byfurther checking with successive sets of range patterns that haveintermediate scores (which identifies defective locations ofintermediate priority), until reaching the set of range patterns thatcorrespond to the smallest score (which yield the lowest prioritydefective locations). The just-described range relaxation is donesystematically, by changing the minimum and maximum limits on the rangeof legal values for each dimension that can vary in a range pattern, toensure that patterns in the layout that would otherwise match a rangepattern are not missed.

Furthermore, as will be apparent to the skilled artisan, severalembodiments of the type described herein result in re-routing of atleast a portion of the layout including a block that matches a rangepattern if at least the lengths of all layout fragments fall within therespective length ranges of the corresponding pattern fragments. Manysuch embodiments perform such re-routing in a prioritized sequence,based scores of respective blocks. After the re-routing is completed,some embodiments use the resulting modified layout to repeat thematching process all over again to find any additional defectivelocations that may now have arisen in view of the re-routing. If in suchrepetition, the same blocks are again targeted, the user is informed sothat excessive looping (to optimize the same block again and again) isavoided.

Moreover, as noted above, some embodiments use two or more disjointranges for a given dimension of a range pattern. For example, the rangepattern shown in FIG. 2A may have two ranges for the dimension “S”namely a first range of 90-120 nm and a second range of 180-210 nm. Inthis example, the first range covers patterns that are known to resultin defective regions, due to minimum spacing requirements whereas thesecond range covers patterns that are poorly realized after fabricationwith sub-resolution assist features (SRAF) due to use of pitches thatare forbidden for use with SRAF (commonly known as “forbidden pitches”).Use of the two disjoint ranges in this example has eliminated the needto define two range patterns that are identical to one another exceptfor the difference in the ranges for the given dimension. Also, notethat some embodiments of range patterns include at least one rectanglethat has two ranges, namely a width range and a length range.

Numerous modifications and adaptations of the embodiments describedherein are encompassed by the scope of the invention.

1. An article of manufacture encoded with a range pattern, said articleof manufacture including a computer-readable medium comprising datarepresenting: a plurality of positions of a corresponding plurality ofline segments in said range pattern; and at least one set of valuescomprising a maximum limit and a minimum limit between which position,relative to one of said line segments, of an additional line segment ofsaid range pattern in a portion of a layout of an integrated circuit(IC) chip, represents a defect in said IC chip when fabricated usingsaid layout.
 2. The article of manufacture of claim 1 wherein said datafurther comprises: a scoring formula representing a change in yield fromfabrication of said IC chip, as a function of a corresponding change insaid position of said additional line segment relative to said maximumlimit and said minimum limit.
 3. The article of manufacture of claim 2wherein: said set of values comprises a value for an optimal distancebetween said maximum limit and said minimum limit; wherein the scoringformula yields a maximum score when said position of said additionalline segment is at said optimal distance.
 4. The article of manufactureof claim 1 wherein: said plurality of ranges conform to design rulechecking (DRC) rules of said fabrication.
 5. The article of manufactureof claim 1 wherein: at least four line segments in said range patternare oriented relative to one another to form a rectangle; and the setcomprises an additional maximum limit and an additional minimum limit ona spacing between said rectangle and an additional rectangle in saidrange pattern.
 6. The article of manufacture of claim 1 wherein: saidmaximum limit and said minimum limit are represented by a boundarybetween two fragments within a slice of said range pattern obtained byslicing said range pattern; each slice in said range pattern is orientedparallel to another slice adjacent thereto; a first fragment in saidslice represents presence of a material in said IC chip and a secondfragment within said slice represents absence of said material, and saidsecond fragment is adjacent to said first fragment.
 7. The article ofmanufacture of claim 6 wherein: said another slice has a third fragment;and dimensions of said third fragment differ from dimensions of each ofsaid first fragment and said second fragment.
 8. The article ofmanufacture of claim 1 futher comprising: a plurality of instructions todetermine if said range pattern is matched by said corresponding portionin said layout.
 9. The article of manufacture of claim 1, wherein: saidcomputer-readable medium comprises a storage medium.
 10. The article ofmanufacture of claim 1 wherein: said maximum limit and said minimumlimit are represented by a width of a slice of said range patternobtained by slicing said range pattern; and each slice in said rangepattern is oriented parallel to another slice adjacent thereto.
 11. Acomputer-implemented method of obtaining a range pattern, the methodcomprising: a computer receiving a position of a plurality of sides of arectangle and at least one pair of limits on one of (position anddimension) of an additional side of said rectangle, wherein saidrectangle is included in said range pattern; said computer using saidlimits in matching said range pattern to a portion of an integratedcircuit (IC) layout; and said computer marking said portion as requiringa change in layout to overcome a fabrication defect.
 12. Thecomputer-implemented method of claim 11 further comprising: saidcomputer receiving an optimal value for said one of (position anddimension) of said additional side; and said computer generating amaximum score for said portion of said layout if a correspondingadditional side in said layout has said optimal value.
 13. Thecomputer-implemented method of claim 11 further comprising: saidcomputer representing said limits in said range pattern by a boundarybetween two fragments in a slice of said range pattern; wherein eachslice is oriented parallel to another slice adjacent thereto, and eachfragment within any slice denotes one of (presence and absence) ofmaterial and any fragment within said any slice that is adjacent to saideach fragment denotes the other of (presence and absence) of material.14. The computer-implemented method of claim 11 further comprising:repeating said computer receiving for at least one additional rectangleincluded in said range pattern.
 15. An article of manufacture encodedwith a range pattern, said article of manufacture including acomputer-readable medium comprising data representing: a plurality oflocations of a corresponding plurality of line segments in said rangepattern; and at least one set of values comprising a maximum limit and aminimum limit between which a dimension of an additional line segment ofsaid range pattern in a portion of a layout of an integrated circuit(IC) chip, represents a defect in said IC chip when fabricated usingsaid layout.
 16. The article of manufacture of claim 15 wherein saiddata further comprises: a scoring formula representing a change in yieldfrom fabrication of said IC chip, as a function of a correspondingchange in said dimension of said additional line segment relative tosaid maximum limit and said minimum limit.
 17. The article ofmanufacture of claim 16 wherein: said set of values comprises a valuefor an optimal distance between said maximum limit and said minimumlimit; wherein the scoring formula yields a maximum score when saiddimension of said additional line segment is at said optimal distance.18. The article of manufacture of claim 17 wherein: at least four linesegments in said range pattern are oriented relative to one another toform a rectangle; said dimension is a width of said rectangle; and saidmaximum limit and said minimum limit are on said width.
 19. The articleof manufacture of claim 18 wherein: the set comprises an additionalmaximum limit and an additional minimum limit on a length of saidrectangle.
 20. The article of manufacture of claim 17 wherein: at leastfour line segments in said range pattern are oriented relative to oneanother to form a rectangle; said dimension is a length of saidrectangle; and said maximum limit and said minimum limit are on saidlength.
 21. The article of manufacture of claim 15 wherein: said maximumlimit and said minimum limit are represented by a boundary between twofragments within a slice of said range pattern obtained by slicing saidrange pattern; each slice in said range pattern is oriented parallel toanother slice adjacent thereto; a first fragment in said slicerepresents presence of a material in said IC chip and a second fragmentwithin said slice represents absence of said material, and said secondfragment is adjacent to said first fragment.
 22. An article ofmanufacture encoded with a range pattern, said article of manufactureincluding a computer-readable medium comprising data representing: aplurality of positions of a corresponding plurality of line segments insaid range pattern; at least one set of values comprising a maximumlimit and a minimum limit; and a constraint on position of at least twoof said line segments; wherein a defect in an integrated circuit (IC)chip is represented by a portion of a layout in said IC chip if: (a)said constraint is satisfied; and (b) said range pattern comprises anadditional line segment at a position between the maximum limit and theminimum limit, relative to one of said line segments.
 23. An article ofmanufacture encoded with a range pattern, said article of manufactureincluding a computer-readable medium comprising data representing: aplurality of positions of a corresponding plurality of line segments insaid range pattern; at least one set of values comprising a maximumlimit and a minimum limit; and a constraint on position of at least twoof said line segments; wherein a defect in an integrated circuit (IC)chip is represented by a portion of a layout in said IC chip if: (a)said constraint is satisfied; and (b) said range pattern comprises anadditional line segment of a dimension between the maximum limit and theminimum limit.